In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes for approximating the extreme positive solutions and the unique positive solution are constructed.
{"title":"Monotone iterative schemes for positive solutions of a fractional differential system with integral boundary conditions on an infinite interval","authors":"Yaohong Li, W. Cheng, Jiafa Xu","doi":"10.2298/FIL2013399L","DOIUrl":"https://doi.org/10.2298/FIL2013399L","url":null,"abstract":"In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes for approximating the extreme positive solutions and the unique positive solution are constructed.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76328286","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}
Pub Date : 2020-05-17DOI: 10.1007/s10476-022-0176-0.pdf
I. Pesenson
{"title":"Jackson theorem and modulus of continuity in Hilbert spaces and on homogeneous manifolds","authors":"I. Pesenson","doi":"10.1007/s10476-022-0176-0.pdf","DOIUrl":"https://doi.org/10.1007/s10476-022-0176-0.pdf","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90677084","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}
Pub Date : 2020-05-13DOI: 10.1016/j.jmaa.2020.124528
Anna Doležalová, Marika Hrubešová, T. Roskovec
{"title":"Hausdorff measure of critical set for Luzin N condition","authors":"Anna Doležalová, Marika Hrubešová, T. Roskovec","doi":"10.1016/j.jmaa.2020.124528","DOIUrl":"https://doi.org/10.1016/j.jmaa.2020.124528","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73723299","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 a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $big(mathcal{H}, langle cdotmid cdotrangle big)$, we consider the semi-Hilbertian space $big(mathcal{H}, langle cdotmid cdotrangle_A big)$ where ${langle xmid yrangle}_A := langle Axmid yrangle$ for every $x, yinmathcal{H}$. The $A$-numerical radius of an $A$-bounded operator $T$ on $mathcal{H}$ is given by begin{align*} omega_A(T) = supBig{big|{langle Txmid xrangle}_Abig|,; ,,xin mathcal{H}, ,{langle xmid xrangle}_A= 1Big}. end{align*} Our aim in this paper is to derive several $mathbb{A}$-numerical radius inequalities for $2times 2$ operator matrices whose entries are $A$-bounded operators, where $mathbb{A}=text{diag}(A,A)$.
{"title":"Some bounds for the $mathbb{A}$-numerical radius of certain $2 times 2$ operator matrices","authors":"Kais Feki","doi":"10.15672/HUJMS.730574","DOIUrl":"https://doi.org/10.15672/HUJMS.730574","url":null,"abstract":"For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $big(mathcal{H}, langle cdotmid cdotrangle big)$, we consider the semi-Hilbertian space $big(mathcal{H}, langle cdotmid cdotrangle_A big)$ where ${langle xmid yrangle}_A := langle Axmid yrangle$ for every $x, yinmathcal{H}$. The $A$-numerical radius of an $A$-bounded operator $T$ on $mathcal{H}$ is given by begin{align*} omega_A(T) = supBig{big|{langle Txmid xrangle}_Abig|,; ,,xin mathcal{H}, ,{langle xmid xrangle}_A= 1Big}. end{align*} Our aim in this paper is to derive several $mathbb{A}$-numerical radius inequalities for $2times 2$ operator matrices whose entries are $A$-bounded operators, where $mathbb{A}=text{diag}(A,A)$.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73944233","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 consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{alpha}$ into Harmonic Bergman-Besov $b^{q}_{beta}$ or weighted Bloch Spaces $b^{infty}_{beta} $, for $1leq pleqinfty$, $1leq q -1$ when $q
我们考虑了在$mathbb{R}^{n}$的单位球上由调和Bergman-Besov核诱导的一类两参数加权积分算子，并精确地描述了那些从Lebesgue空间$L^{p}_{alpha}$入调和Bergman-Besov $b^{q}_{beta}$或加权Bloch空间$b^{infty}_{beta} $的算子，对于$1leq pleqinfty$，通过将算子映射到这些空间而不是映射到Lebesgue类上的调和Bergman-Besov核诱导的一类积分算子$1leq q -1$ when $q
{"title":"A class of Integral Operators from Lebesgue spaces into Harmonic Bergman-Besov or Weighted Bloch Spaces","authors":"Ö. Doğan","doi":"10.15672/HUJMS.768123","DOIUrl":"https://doi.org/10.15672/HUJMS.768123","url":null,"abstract":"We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{alpha}$ into Harmonic Bergman-Besov $b^{q}_{beta}$ or weighted Bloch Spaces $b^{infty}_{beta} $, for $1leq pleqinfty$, $1leq q -1$ when $q<infty$ and $betageq 0$ when $q=infty$ of Dogan (A Class of Integral Operators Induced by Harmonic Bergman-Besov kernels on Lebesgue Classes, preprint, 2020) by mapping the operators into these spaces instead of the Lebesgue classes.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89932161","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}
Simone Di Marino, Danka Luvci'c, Enrico Pasqualetto
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
{"title":"A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space","authors":"Simone Di Marino, Danka Luvci'c, Enrico Pasqualetto","doi":"10.5802/crmath.88","DOIUrl":"https://doi.org/10.5802/crmath.88","url":null,"abstract":"We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78940451","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}
Eva A. Gallardo-Guti'errez, Javier Gonz'alez-Dona, P. Tradacete
We prove that every lattice homomorphism acting on a Banach space $mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these later examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on $mathcal{X}$ extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.
{"title":"Invariant subspaces for positive operators on Banach spaces with unconditional basis","authors":"Eva A. Gallardo-Guti'errez, Javier Gonz'alez-Dona, P. Tradacete","doi":"10.1090/proc/16026","DOIUrl":"https://doi.org/10.1090/proc/16026","url":null,"abstract":"We prove that every lattice homomorphism acting on a Banach space $mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these later examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on $mathcal{X}$ extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91403020","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 prove that a Banach space of continuous functions $C(K)$ has a renorming that is uniformly rotund in every direction (URED) if and only if the compact space $K$ supports a strictly positive measure
{"title":"Spaces 𝐶(𝐾) with an equivalent URED norm","authors":"A. Avil'es, S. Troyanski","doi":"10.1090/proc/15315","DOIUrl":"https://doi.org/10.1090/proc/15315","url":null,"abstract":"We prove that a Banach space of continuous functions $C(K)$ has a renorming that is uniformly rotund in every direction (URED) if and only if the compact space $K$ supports a strictly positive measure","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90146090","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 prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikodým property. We also show that the Lipschitz free space over a complete, locally compact metric space has the Schur or approximation property whenever the Lipschitz free space over each compact subset also has this property.
{"title":"Lipschitz free spaces over locally compact metric spaces","authors":"C. Gartland","doi":"10.4064/SM200511-10-10","DOIUrl":"https://doi.org/10.4064/SM200511-10-10","url":null,"abstract":"We prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikodým property. We also show that the Lipschitz free space over a complete, locally compact metric space has the Schur or approximation property whenever the Lipschitz free space over each compact subset also has this property.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85910807","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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