We prove a real version of the Lax-Phillips Theorem and classify outgoing reflection positive orthogonal one-parameter groups. Using these results, we provide a normal form for outgoing monotone geodesics in the set Stand(H) of standard subspaces on some complex Hilbert space H. As the modular operators of a standard subspace are closely related to positive Hankel operators, our results are obtained by constructing some explicit symbols for positive Hankel operators. We also describe which of the monotone geodesics in Stand(H) arise from the unitary one-parameter groups described in Borchers' Theorem and provide explicit examples of monotone geodesics that are not of this type.
我们证明了拉克斯-菲利普斯定理的真实版本，并对出射反射正交单参数群进行了分类。利用这些结果，我们为某个复希尔伯特空间 H 上的标准子空间集合 Stand(H) 中的出射单调大地线提供了一个正则表达式。由于标准子空间的模算子与正汉克尔算子密切相关，我们的结果是通过构造正汉克尔算子的一些显式符号得到的。我们还描述了Stand(H)中哪些单调大地线是由Borchers定理中描述的单元单参数群产生的，并提供了不属于这种类型的单调大地线的明确例子。
{"title":"Outgoing monotone geodesics of standard subspaces","authors":"Jonas Schober","doi":"arxiv-2409.08184","DOIUrl":"https://doi.org/arxiv-2409.08184","url":null,"abstract":"We prove a real version of the Lax-Phillips Theorem and classify outgoing\u0000reflection positive orthogonal one-parameter groups. Using these results, we\u0000provide a normal form for outgoing monotone geodesics in the set Stand(H) of\u0000standard subspaces on some complex Hilbert space H. As the modular operators of\u0000a standard subspace are closely related to positive Hankel operators, our\u0000results are obtained by constructing some explicit symbols for positive Hankel\u0000operators. We also describe which of the monotone geodesics in Stand(H) arise\u0000from the unitary one-parameter groups described in Borchers' Theorem and\u0000provide explicit examples of monotone geodesics that are not of this type.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this article is to introduce the H-infinity functional calculus for unbounded bisectorial operators in a Clifford module over the algebra R_n. While recent studies have focused on bounded operators or unbounded paravector operators, we now investigate unbounded fully Clifford operators and define polynomially growing functions of them. We first generate the omega-functional calculus for functions that exhibit an appropriate decay at zero and at infinity. We then extend to functions with a finite value at zero and at infinity. Finally, using a subsequent regularization procedure, we can define the H-infinity functional calculus for the class of regularizable functions, which in particular include functions with polynomial growth at infinity and, if T is injective, also functions with polynomial growth at zero.
本文旨在介绍代数 R_n 上克利福德模中无界二叉算子的 H-infinity 函数微积分。最近的研究主要集中于有界算子或无界旁向量算子，而我们现在研究的是无界全克利福德算子，并定义它们的波函数。我们首先为在零点和无限点表现出适当衰减的函数生成欧米伽函数微积分。然后，我们将其扩展到在零点和无限点具有有限值的函数。最后，利用随后的正则化过程，我们可以为一类可正则化函数定义 H-infinity 函数微积分，这一类函数尤其包括在无穷处具有多项式增长的函数，如果 T 是注入式的，还包括在零处具有多项式增长的函数。
{"title":"The $H^infty$-functional calculus for bisectorial Clifford operators","authors":"Francesco Mantovani, Peter Schlosser","doi":"arxiv-2409.07249","DOIUrl":"https://doi.org/arxiv-2409.07249","url":null,"abstract":"The aim of this article is to introduce the H-infinity functional calculus\u0000for unbounded bisectorial operators in a Clifford module over the algebra R_n.\u0000While recent studies have focused on bounded operators or unbounded paravector\u0000operators, we now investigate unbounded fully Clifford operators and define\u0000polynomially growing functions of them. We first generate the omega-functional\u0000calculus for functions that exhibit an appropriate decay at zero and at\u0000infinity. We then extend to functions with a finite value at zero and at\u0000infinity. Finally, using a subsequent regularization procedure, we can define\u0000the H-infinity functional calculus for the class of regularizable functions,\u0000which in particular include functions with polynomial growth at infinity and,\u0000if T is injective, also functions with polynomial growth at zero.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we proved that $T_{z^n}$ acting on the $mathbb{C}^m$-valued Hardy space $H_{mathbb{C}^m}^2(mathbb{D})$, is unitarily equivalent to $bigoplus_1^{mn}T_z$, where $T_z$ is acting on the scalar-valued Hardy space $H_{mathbb{C}}^2(mathbb{D})$. And using the matrix manipulations combined with operator theory methods, we completely describe the reducing subspaces of $T_{z^n}$ on $H_{mathbb{C}^m}^2(mathbb{D})$.
{"title":"On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space","authors":"Cui Chen, Yucheng Li, Ya Wang","doi":"arxiv-2409.07112","DOIUrl":"https://doi.org/arxiv-2409.07112","url":null,"abstract":"In this paper, we proved that $T_{z^n}$ acting on the $mathbb{C}^m$-valued\u0000Hardy space $H_{mathbb{C}^m}^2(mathbb{D})$, is unitarily equivalent to\u0000$bigoplus_1^{mn}T_z$, where $T_z$ is acting on the scalar-valued Hardy space\u0000$H_{mathbb{C}}^2(mathbb{D})$. And using the matrix manipulations combined\u0000with operator theory methods, we completely describe the reducing subspaces of\u0000$T_{z^n}$ on $H_{mathbb{C}^m}^2(mathbb{D})$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"175 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce and study the notion of hereditary frequent hypercyclicity, which is a reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for the study of the dynamical properties of direct sums of operators; in particular, a basic observation is that the direct sum of a hereditarily frequently hypercyclic operator with any frequently hypercyclic operator is frequently hypercyclic. Among other results, we show that operators satisfying the Frequent Hypercyclicity Criterion are hereditarily frequently hypercyclic, as well as a large class of operators whose unimodular eigenvectors are spanning with respect to the Lebesgue measure. On the other hand, we exhibit two frequently hypercyclic weighted shifts $B_w,B_{w'}$ on $c_0(mathbb{Z}_+)$ whose direct sum $B_woplus B_{w'}$ is not $mathcal{U}$-frequently hypercyclic (so that neither of them is hereditarily frequently hypercyclic), and we construct a $C$-type operator on $ell_p(mathbb{Z}_+)$, $1le p
我们引入并研究了遗传频繁超周期性的概念，它是对众所周知的频繁超周期性概念的强化。这个概念对于研究算子直接和的动力学性质非常有用；特别是，一个基本观察结果是，遗传频繁超周期算子与任何频繁超周期算子的直接和是频繁超周期的。除其他结果外，我们还证明了满足频繁超循环准则的算子是遗传频繁超循环的，以及一大类算子，它们的单模态特征向量相对于 Lebesgue 度量是遍及的。另一方面，我们展示了$c_0(mathbb{Z}_+)$上两个频繁超循环的加权移$B_w,B_{w'}$，它们的直接和$B_woplus B_{w'}$不是$mathcal{U}$-频繁超循环的（因此它们都不是遗传频繁超循环的）、我们在$ell_p(mathbb{Z}_+)$上构造了一个$C$型算子，$1le p
{"title":"Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity","authors":"F. Bayart, S. Grivaux, E. Matheron, Q. Menet","doi":"arxiv-2409.07103","DOIUrl":"https://doi.org/arxiv-2409.07103","url":null,"abstract":"We introduce and study the notion of hereditary frequent hypercyclicity,\u0000which is a reinforcement of the well known concept of frequent hypercyclicity.\u0000This notion is useful for the study of the dynamical properties of direct sums\u0000of operators; in particular, a basic observation is that the direct sum of a\u0000hereditarily frequently hypercyclic operator with any frequently hypercyclic\u0000operator is frequently hypercyclic. Among other results, we show that operators\u0000satisfying the Frequent Hypercyclicity Criterion are hereditarily frequently\u0000hypercyclic, as well as a large class of operators whose unimodular\u0000eigenvectors are spanning with respect to the Lebesgue measure. On the other\u0000hand, we exhibit two frequently hypercyclic weighted shifts $B_w,B_{w'}$ on\u0000$c_0(mathbb{Z}_+)$ whose direct sum $B_woplus B_{w'}$ is not\u0000$mathcal{U}$-frequently hypercyclic (so that neither of them is hereditarily\u0000frequently hypercyclic), and we construct a $C$-type operator on\u0000$ell_p(mathbb{Z}_+)$, $1le p<infty$ which is frequently hypercyclic but not\u0000hereditarily frequently hypercyclic. We also solve several problems concerning\u0000disjoint frequent hypercyclicity: we show that for every $Ninmathbb{N}$, any\u0000disjoint frequently hypercyclic $N$-tuple of operators $(T_1,dots ,T_N)$ can\u0000be extended to a disjoint frequently hypercyclic $(N+1)$-tuple $(T_1,dots\u0000,T_N, T_{N+1})$ as soon as the underlying space supports a hereditarily\u0000frequently hypercyclic operator; we construct a disjoint frequently hypercyclic\u0000pair which is not densely disjoint hypercyclic; and we show that the pair\u0000$(D,tau_a)$ is disjoint frequently hypercyclic, where $D$ is the derivation\u0000operator acting on the space of entire functions and $tau_a$ is the operator\u0000of translation by $ainmathbb{C}setminus{ 0}$. Part of our results are in\u0000fact obtained in the general setting of Furstenberg families.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms on the upper half-space previously considered in the literature. Comparing the resulting function spaces to known function spaces such as $dot{W}^{1,p}(rn)$, $JNp$, $Lp$ and weak-$Lp$ gives new embeddings and characterizations of these spaces. Examples are provided to prove the sharpness of the results.
{"title":"A Dyadic Approach to Weak Characterizations of Function Spaces","authors":"Galia Dafni, Shahaboddin Shaabani","doi":"arxiv-2409.07395","DOIUrl":"https://doi.org/arxiv-2409.07395","url":null,"abstract":"Weak-type quasi-norms are defined using the mean oscillation or the mean of a\u0000function on dyadic cubes, providing discrete analogues and variants of the\u0000corresponding quasi-norms on the upper half-space previously considered in the\u0000literature. Comparing the resulting function spaces to known function spaces\u0000such as $dot{W}^{1,p}(rn)$, $JNp$, $Lp$ and weak-$Lp$ gives new embeddings\u0000and characterizations of these spaces. Examples are provided to prove the\u0000sharpness of the results.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we first introduce $mathbb{L}$-$mu$-measurable functions and $mathbb{L}$-Bochner integrable functions on a finite measure space $(S,mathcal{F},mu),$ and give an $mathbb{L}$-valued analogue of the canonical $L^{p}(Omega,mathcal{F},mu).$ Then we investigate the completeness of such an $mathbb{L}$-valued analogue and propose the Radon-Nikod$acute{y}$m property of $mathbb{L}$-Banach spaces. Meanwhile, an example constructed in this paper shows that there do exist an $mathbb{L}$-Banach space which fails to possess the Radon-Nikod$acute{y}$m property. Finally, based on above work, we establish the dual representation theorem of $mathbb{L}$-Bochner integrable function spaces, which extends and improves the corresponding classical result.
{"title":"The Radon-Nikod$acute{Y}$m property of $mathbb{L}$-Banach spaces and the dual representation theorem of $mathbb{L}$-Bochner function spaces","authors":"Xia Zhang, Xiangle Yan, Ming Liu","doi":"arxiv-2409.06279","DOIUrl":"https://doi.org/arxiv-2409.06279","url":null,"abstract":"In this paper, we first introduce $mathbb{L}$-$mu$-measurable functions and\u0000$mathbb{L}$-Bochner integrable functions on a finite measure space\u0000$(S,mathcal{F},mu),$ and give an $mathbb{L}$-valued analogue of the\u0000canonical $L^{p}(Omega,mathcal{F},mu).$ Then we investigate the completeness\u0000of such an $mathbb{L}$-valued analogue and propose the Radon-Nikod$acute{y}$m\u0000property of $mathbb{L}$-Banach spaces. Meanwhile, an example constructed in\u0000this paper shows that there do exist an $mathbb{L}$-Banach space which fails\u0000to possess the Radon-Nikod$acute{y}$m property. Finally, based on above work,\u0000we establish the dual representation theorem of $mathbb{L}$-Bochner integrable\u0000function spaces, which extends and improves the corresponding classical result.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"317 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wolfgang Bock, Ang Elyn Gumanoy, Sheila Menchavez, Elmira Nabizadeh Morsalfard
In this paper, we provide proofs for the analytic characterization theorems of the operator symbols utilizing the characterization theorem for the Mittag-Leffler distribution space.We work out examples which can be interpreted as integral kernel operators and treat the important case of the translation operator.
{"title":"An analytic characterization of symbols of operators on non-Gaussian Mittag-Leffler functionals","authors":"Wolfgang Bock, Ang Elyn Gumanoy, Sheila Menchavez, Elmira Nabizadeh Morsalfard","doi":"arxiv-2409.06143","DOIUrl":"https://doi.org/arxiv-2409.06143","url":null,"abstract":"In this paper, we provide proofs for the analytic characterization theorems\u0000of the operator symbols utilizing the characterization theorem for the\u0000Mittag-Leffler distribution space.We work out examples which can be interpreted\u0000as integral kernel operators and treat the important case of the translation\u0000operator.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For $pin [1,infty]$, we define a smooth manifold structure on the set of absolutely continuous functions $gammacolon [a,b]to N$ with $L^p$-derivatives for each smooth manifold $N$ modeled on a sequentially complete locally convex topological vector space which admits a local addition. Smoothness of natural mappings between spaces of absolutely continuous functions is discussed. For $1leq p
对于 $pin [1,infty]$，我们在绝对连续函数的集合上定义了一个光滑流形结构。对于$1leq p
{"title":"Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups","authors":"Matthieu F. Pinaud","doi":"arxiv-2409.06512","DOIUrl":"https://doi.org/arxiv-2409.06512","url":null,"abstract":"For $pin [1,infty]$, we define a smooth manifold structure on the set of\u0000absolutely continuous functions $gammacolon [a,b]to N$ with\u0000$L^p$-derivatives for each smooth manifold $N$ modeled on a sequentially\u0000complete locally convex topological vector space which admits a local addition.\u0000Smoothness of natural mappings between spaces of absolutely continuous\u0000functions is discussed. For $1leq p <infty$ and $rin mathbb{N}$ we show\u0000that the right half-Lie groups $text{Diff}_K(mathbb{R})$ and $text{Diff}(M)$\u0000are $L^p$-semiregular. Here $K$ is a compact subset of $mathbb{R}^n$ and $M$\u0000is a compact smooth manifold. For the preceding examples, the evolution map\u0000$text{Evol}$ is continuous.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The maximal hyperplane section of the $l_infty^n$-ball, i.e. of the $n$-cube, is the one perpendicular to 1/sqrt 2 (1,1,0, ... ,0), as shown by Ball. Eskenazis, Nayar and Tkocz extended this result to the $l_p^n$-balls for very large $p ge 10^{15}$. We show that the analogue of Ball's result essentially holds for all $26.265 simeq p_0 le p < infty$. By Oleszkiewicz, Ball's result does not transfer to $l_p^n$ for $2 < p < p_0$. Then the hyperplane section perpendicular to the main diagonal yields a counterexample for large dimensions $n$. In this case, we give an asymptotic upper bound for $20 < p < p_0$.
正如鲍尔所证明的，$l_infty^n$球，即$n$立方体的最大超平面截面是垂直于 1/sqrt 2 (1,1,0, ... ,0)的截面。Eskenazis, Nayar 和 Tkocz 将这一结果扩展到了非常大的 $p ge 10^{15}$ 的 $l_p^n$-球。我们证明，波尔的类似结果基本上对所有 $26.265 simeq p_0 le p < infty$都成立。根据 Oleszkiewicz 的观点，波尔的结果在 $2 < p < p_0$ 时并不转移到 $l_p^n$。那么，垂直于主对角线的超平面截面在维数 $n$ 较大时会产生一个反例。在这种情况下，我们给出了$20 < p < p_0$ 的渐近上界。
{"title":"Maximal hyperplane sections of the unit ball of $l_p$ for $p>2$","authors":"Hermann König","doi":"arxiv-2409.06432","DOIUrl":"https://doi.org/arxiv-2409.06432","url":null,"abstract":"The maximal hyperplane section of the $l_infty^n$-ball, i.e. of the\u0000$n$-cube, is the one perpendicular to 1/sqrt 2 (1,1,0, ... ,0), as shown by\u0000Ball. Eskenazis, Nayar and Tkocz extended this result to the $l_p^n$-balls for\u0000very large $p ge 10^{15}$. We show that the analogue of Ball's result\u0000essentially holds for all $26.265 simeq p_0 le p < infty$. By Oleszkiewicz,\u0000Ball's result does not transfer to $l_p^n$ for $2 < p < p_0$. Then the\u0000hyperplane section perpendicular to the main diagonal yields a counterexample\u0000for large dimensions $n$. In this case, we give an asymptotic upper bound for\u0000$20 < p < p_0$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that if a separable Banach space has Kalton's property $(M^ast)$, then all $varepsilon$-Szlenk derivations of the dual unit ball are balls, however, in the case of the dual of Baernstein's space, all those Szlenk derivations are balls having the same radius as for $ell_2$, yet this space fails property $(M^ast)$. By estimating the radii of enveloping balls, we show that the Szlenk derivations are not balls for Tsirelson's space and the dual of Schlumprecht's space. Using the Karush-Kuhn-Tucker theorem we prove that the same is true for the duals of certain sequential Orlicz spaces.
{"title":"When is the Szlenk derivation of a dual unit ball another ball?","authors":"Tomasz Kochanek, Marek Miarka","doi":"arxiv-2409.05516","DOIUrl":"https://doi.org/arxiv-2409.05516","url":null,"abstract":"We show that if a separable Banach space has Kalton's property $(M^ast)$,\u0000then all $varepsilon$-Szlenk derivations of the dual unit ball are balls,\u0000however, in the case of the dual of Baernstein's space, all those Szlenk\u0000derivations are balls having the same radius as for $ell_2$, yet this space\u0000fails property $(M^ast)$. By estimating the radii of enveloping balls, we show\u0000that the Szlenk derivations are not balls for Tsirelson's space and the dual of\u0000Schlumprecht's space. Using the Karush-Kuhn-Tucker theorem we prove that the\u0000same is true for the duals of certain sequential Orlicz spaces.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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