Pub Date : 2024-07-06DOI: 10.1080/03081087.2024.2368734
Roman Drnovšek
Let T be an operator on a Banach space X that is similar to −T via an involution U. Then,U decomposes the Banach space X as X=X1⊕X2 with respect to which decomposition we have U=(I100−I2), where Ii...
让 T 是巴拿赫空间 X 上的一个算子，通过内卷 U 与 -T 相似。那么，U 将巴拿赫空间 X 分解为 X=X1⊕X2，关于该分解，我们有 U=(I100-I2)，其中 Ii...
{"title":"On commutators of idempotents","authors":"Roman Drnovšek","doi":"10.1080/03081087.2024.2368734","DOIUrl":"https://doi.org/10.1080/03081087.2024.2368734","url":null,"abstract":"Let T be an operator on a Banach space X that is similar to −T via an involution U. Then,U decomposes the Banach space X as X=X1⊕X2 with respect to which decomposition we have U=(I100−I2), where Ii...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141618195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-03DOI: 10.1080/03081087.2024.2368240
M. J. de la Puente, P. L. Clavería
In any dimension d≥2, we give exact volume formulas of two mutually polar dual convex d-polytopes. The primal body is called isocanted cube of dimension d, depending on two real parameters 0
在任意维数 d≥2 时，我们给出了两个互为极性的对偶凸 d 多面体的精确体积公式。基元体被称为维数为 d 的等位立方体，取决于两个实数参数 0
{"title":"The volume of an isocanted cube is a determinant*","authors":"M. J. de la Puente, P. L. Clavería","doi":"10.1080/03081087.2024.2368240","DOIUrl":"https://doi.org/10.1080/03081087.2024.2368240","url":null,"abstract":"In any dimension d≥2, we give exact volume formulas of two mutually polar dual convex d-polytopes. The primal body is called isocanted cube of dimension d, depending on two real parameters 0<a<ℓ. T...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141608156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1080/03081087.2024.2366951
Florian Bünger, Alberto Seeger
Let n∈N, K∈{R,C} and Mn(K) be the set of all n-by-n matrices with entries in K. We investigate the sensitivity of the generalized spectral radius ρK(A):=max{|λ|:λ∈Kand|Ax|=|λx|foranx∈Kn∖{0}} of A∈...
假设 n∈N，K∈{R,C}，Mn(K) 是所有 n-by-n 矩阵的集合，其条目在 K 中。我们研究了 A∈ 的广义谱半径 ρK(A):=max{|λ|:λ∈Kand|Ax|=|λx|foranx∈Kn∖{0}}的敏感性。
{"title":"Perturbation properties of the generalized spectral radius","authors":"Florian Bünger, Alberto Seeger","doi":"10.1080/03081087.2024.2366951","DOIUrl":"https://doi.org/10.1080/03081087.2024.2366951","url":null,"abstract":"Let n∈N, K∈{R,C} and Mn(K) be the set of all n-by-n matrices with entries in K. We investigate the sensitivity of the generalized spectral radius ρK(A):=max{|λ|:λ∈Kand|Ax|=|λx|foranx∈Kn∖{0}} of A∈...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141425526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.1080/03081087.2024.2362194
A. T. Mithun
We present a new method to construct symmetric symbols corresponding to solvable multiscaling equations using linear operators. First, we define a linear operator corresponding to a symbol. We demo...
{"title":"Linear operators and construction of symmetric symbols satisfying sum rules of order p","authors":"A. T. Mithun","doi":"10.1080/03081087.2024.2362194","DOIUrl":"https://doi.org/10.1080/03081087.2024.2362194","url":null,"abstract":"We present a new method to construct symmetric symbols corresponding to solvable multiscaling equations using linear operators. First, we define a linear operator corresponding to a symbol. We demo...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.1080/03081087.2024.2353785
Bing Yang, Chengjun Hou, Xiaochun Fang
We prove that if Δ is a norm-continuous weak∗-2-local derivation on a von Neumann algebra M and satisfies Δ(p+iμq)=Δ(p)+iμΔ(q) for every pair of projections p and q in M, and every μ∈R, then Δ is a...
{"title":"2-local S mappings with respect to τ on some *-subalgebras of","authors":"Bing Yang, Chengjun Hou, Xiaochun Fang","doi":"10.1080/03081087.2024.2353785","DOIUrl":"https://doi.org/10.1080/03081087.2024.2353785","url":null,"abstract":"We prove that if Δ is a norm-continuous weak∗-2-local derivation on a von Neumann algebra M and satisfies Δ(p+iμq)=Δ(p)+iμΔ(q) for every pair of projections p and q in M, and every μ∈R, then Δ is a...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141430485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-04DOI: 10.1080/03081087.2024.2349197
Paola Boito, G. M. Del Corso
In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known ...
{"title":"Quantum hitting time according to a given distribution","authors":"Paola Boito, G. M. Del Corso","doi":"10.1080/03081087.2024.2349197","DOIUrl":"https://doi.org/10.1080/03081087.2024.2349197","url":null,"abstract":"In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known ...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141425403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-27DOI: 10.1080/03081087.2024.2352456
Chia-Yu Chang
We prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.
我们证明了最大边界子级张量集合维数的下限。这是第一个此类下限。
{"title":"Maximal border subrank tensors","authors":"Chia-Yu Chang","doi":"10.1080/03081087.2024.2352456","DOIUrl":"https://doi.org/10.1080/03081087.2024.2352456","url":null,"abstract":"We prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141315628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-20DOI: 10.1080/03081087.2024.2356827
Clément de Seguins Pazzis
Let F be a field, and n≥r>0 be integers, with r even. Denote by An(F) the space of all n-by-n alternating matrices with entries in F. We consider the problem of determining the greatest possible d...
设 F 是一个域，n≥r>0 为整数，其中 r 为偶数。用 An(F) 表示条目在 F 中的所有 n-by-n 交替矩阵的空间。
{"title":"On affine spaces of alternating matrices with constant rank","authors":"Clément de Seguins Pazzis","doi":"10.1080/03081087.2024.2356827","DOIUrl":"https://doi.org/10.1080/03081087.2024.2356827","url":null,"abstract":"Let F be a field, and n≥r>0 be integers, with r even. Denote by An(F) the space of all n-by-n alternating matrices with entries in F. We consider the problem of determining the greatest possible d...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-20DOI: 10.1080/03081087.2024.2352465
Cong Trinh Le, The Khoi Vu, Minh Toan Ho, Trung Hoa Dinh
In this article, we investigate explicitly the minimal and maximal values of the α-z-Rényi divergences and some other types of Rényi divergences between unitary orbits. Our main tools are the major...
{"title":"Optimization of some types of Rényi divergences between unitary orbits","authors":"Cong Trinh Le, The Khoi Vu, Minh Toan Ho, Trung Hoa Dinh","doi":"10.1080/03081087.2024.2352465","DOIUrl":"https://doi.org/10.1080/03081087.2024.2352465","url":null,"abstract":"In this article, we investigate explicitly the minimal and maximal values of the α-z-Rényi divergences and some other types of Rényi divergences between unitary orbits. Our main tools are the major...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1080/03081087.2024.2352776
Raffaella Cilia, Joaquín M. Gutiérrez
Let μ be a finite measure, T:L1(μ)→X be an operator into a Banach space X, and I:L∞(μ)→L1(μ) be the natural inclusion. A well-known theorem due to Grothendieck states that T is representable if and...
设 μ 是有限度量，T:L1(μ)→X 是进入巴拿赫空间 X 的算子，I:L∞(μ)→L1(μ) 是自然包含。格罗登第克提出的一个著名定理指出，如果且...
{"title":"Grothendieck-type characterization of representable multilinear mappings","authors":"Raffaella Cilia, Joaquín M. Gutiérrez","doi":"10.1080/03081087.2024.2352776","DOIUrl":"https://doi.org/10.1080/03081087.2024.2352776","url":null,"abstract":"Let μ be a finite measure, T:L1(μ)→X be an operator into a Banach space X, and I:L∞(μ)→L1(μ) be the natural inclusion. A well-known theorem due to Grothendieck states that T is representable if and...","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141092015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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