Studia Mathematica最新文献

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Essential numerical range and $C$-numerical rangefor unbounded operators 无界运算符的基本数值范围和$C$-数值范围
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2022-01-01 DOI: 10.4064/sm201231-16-9
N. Hefti, C. Tretter
{"title":"Essential numerical range and $C$-numerical range\u0000for unbounded operators","authors":"N. Hefti, C. Tretter","doi":"10.4064/sm201231-16-9","DOIUrl":"https://doi.org/10.4064/sm201231-16-9","url":null,"abstract":". We introduce two new concepts for unbounded operators T in a Hilbert space, the essential numerical range W e 5 ( T ) of type 5 and the C -numerical range W C ( T ) . Our first main result clarifies the relation of W e 5 ( T ) to the essential numerical range W e ( T ) , answering an open problem of Bögli, Marletta and Tretter’s (2020) by employing the Bessaga–Pełczyński selection theorem from Banach space theory. It turns out that W e 5 ( T ) ⊂ W e ( T ) and we establish sharp conditions for equality. An example for strict inclusion shows that W e ( T ) may be a half-plane, while W e 5 ( T ) only a line. We also show that W e 5 ( T ) is convex and that it contains the convex hull of the essential spectrum. Our second main result reveals a geometric relation between W e 5 ( T ) and W C ( T ) . We show that, for finite-rank operators C , W C ( T ) is star-shaped with star-centre (Tr C ) W e 5 ( T ) , generalizing a result for bounded operators where W e 5 ( T ) = W e ( T ) .","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Trotter–Kato product formula in symmetric F-normed ideals 对称f赋范理想中的Trotter-Kato积公式
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2022-01-01 DOI: 10.4064/sm210708-4-11
Meiram Akhymbek, G. Levitina
{"title":"Trotter–Kato product formula in symmetric F-normed ideals","authors":"Meiram Akhymbek, G. Levitina","doi":"10.4064/sm210708-4-11","DOIUrl":"https://doi.org/10.4064/sm210708-4-11","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The Mazur–Ulam property for abelian $C^*$-algebras 阿贝尔代数C^* -代数的Mazur-Ulam性质
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2022-01-01 DOI: 10.4064/sm210709-6-12
Ruidong Wang, Yuexing Niu
{"title":"The Mazur–Ulam property for abelian $C^*$-algebras","authors":"Ruidong Wang, Yuexing Niu","doi":"10.4064/sm210709-6-12","DOIUrl":"https://doi.org/10.4064/sm210709-6-12","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
On the Semadeni derivative of Banach spaces $C(K,X)$ Banach空间C(K,X)的Semadeni导数
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2022-01-01 DOI: 10.4064/sm210810-9-12
Leandro Candido
{"title":"On the Semadeni derivative of Banach spaces $C(K,X)$","authors":"Leandro Candido","doi":"10.4064/sm210810-9-12","DOIUrl":"https://doi.org/10.4064/sm210810-9-12","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterizations of Daugavet points and delta-pointsin Lipschitz-free spaces 无lipschitz空间中道格瓦点和δ点的刻画
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2022-01-01 DOI: 10.4064/sm220207-30-4
Triinu Veeorg
{"title":"Characterizations of Daugavet points and delta-points\u0000in Lipschitz-free spaces","authors":"Triinu Veeorg","doi":"10.4064/sm220207-30-4","DOIUrl":"https://doi.org/10.4064/sm220207-30-4","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70525074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Kato’s inequality for the strong $p(cdot)$-Laplacian 强$p(cdot)$-拉普拉斯不等式的加藤不等式
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2022-01-01 DOI: 10.4064/sm220330-19-9
T. Do, L. Truong
{"title":"Kato’s inequality for the strong $p(cdot)$-Laplacian","authors":"T. Do, L. Truong","doi":"10.4064/sm220330-19-9","DOIUrl":"https://doi.org/10.4064/sm220330-19-9","url":null,"abstract":"","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weak$^*$ closures and derived sets for convex sets in dual Banach spaces 对偶Banach空间中凸集的弱$^*$闭包和导集
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-12-09 DOI: 10.4064/sm211211-25-6
M. Ostrovskii
{"title":"Weak$^*$ closures and derived sets for convex sets in dual Banach spaces","authors":"M. Ostrovskii","doi":"10.4064/sm211211-25-6","DOIUrl":"https://doi.org/10.4064/sm211211-25-6","url":null,"abstract":"Abstract: The paper is devoted to the convex-set counterpart of the theory of weak derived sets initiated by Banach and Mazurkiewicz for subspaces. The main result is the following: For every nonreflexive Banach space X and every countable successor ordinal α, there exists a convex subset A in X such that α is the least ordinal for which the weak derived set of order α coincides with the weak closure of A. This result extends the previously known results on weak derived sets by Ostrovskii (2011) and Silber (2021).","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46726858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Extension of $c_0(I)$-valued operators on spaces ofcontinuous functions on compact lines 紧致线上连续函数空间上$c_0(I)$-value算子的推广
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-11-20 DOI: 10.4064/sm211120-2-6
Victor dos Santos Ronchim, D. Tausk
{"title":"Extension of $c_0(I)$-valued operators on spaces of\u0000continuous functions on compact lines","authors":"Victor dos Santos Ronchim, D. Tausk","doi":"10.4064/sm211120-2-6","DOIUrl":"https://doi.org/10.4064/sm211120-2-6","url":null,"abstract":". We investigate the problem of existence of a bounded extension to C ( K ) of a bounded c 0 ( I )-valued operator T defined on the subalgebra of C ( K ) induced by a continuous increasing surjection φ : K → L , where K and L are compact lines. Generalizations of some of the results of [6] about extension of c 0 -valued operators are obtained. For instance, we prove that when a bounded extension of T exists then an extension can be obtained with norm at most twice the norm of T . Moreover, the class of compact lines L for which the c 0 -extension property is equivalent to the c 0 ( I )-extension property for any continuous increasing surjection φ : K → L is studied.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46673693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random Lochs’ Theorem 随机洛克定理
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-10-27 DOI: 10.4064/sm211028-24-2
Charlene Kalle, E. Verbitskiy, B. Zeegers
{"title":"Random Lochs’ Theorem","authors":"Charlene Kalle, E. Verbitskiy, B. Zeegers","doi":"10.4064/sm211028-24-2","DOIUrl":"https://doi.org/10.4064/sm211028-24-2","url":null,"abstract":"Abstract. In 1964 Lochs proved a theorem on the number of continued fraction digits of a real number x that can be determined from just knowing its first n decimal digits. In 2001 this result was generalised to a dynamical systems setting by Dajani and Fieldsteel, where it compares sizes of cylinder sets for different transformations. In this article we prove a version of Lochs’ Theorem for random dynamical systems as well as a corresponding Central Limit Theorem. The main ingredient for the proof is an estimate on the asymptotic size of the cylinder sets of the random system in terms of the fiber entropy. To compute this entropy we provide a random version of Rokhlin’s formula for entropy.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Compact multiplication operators on semicrossed products 半交叉积上的紧乘算子
IF 0.8 3区 数学
Studia Mathematica Pub Date : 2021-10-14 DOI: 10.4064/sm211107-22-7
G. Andreolas, M. Anoussis, C. Magiatis
{"title":"Compact multiplication operators on semicrossed products","authors":"G. Andreolas, M. Anoussis, C. Magiatis","doi":"10.4064/sm211107-22-7","DOIUrl":"https://doi.org/10.4064/sm211107-22-7","url":null,"abstract":"Let A be a Banach algebra and a, b ∈ A. The map Ma,b : A → A given by Ma,b(x) = axb is called a multiplication operator. Properties of compact multiplication operators have been investigated since 1964 when Vala published his work “On compact sets of compact operators” [15]. Let X be a normed space and B(X ) the algebra of all bounded linear maps from X into X . Vala proved that a nonzero multiplication operator Ma,b : B(X ) → B(X ) is compact if and only if the operators a, b ∈ B(X ) are both compact. Also, in [16] Vala defines an element a of a normed algebra to be compact if the mapping x 7→ axa is compact. This concept enabled the study of compactness properties of elements of abstract normed algebras. Ylinen in [17] studied compact elements for abstract C*-algebras and showed that a is a compact element of a C-algebra A if and only if there exists an isometric ∗-representation π of A on a Hilbert space H such that the operator π(a) is compact. Compactness questions have also been considered in the more general framework of elementary operators. A map Φ : A → A, where A is a Banach algebra, is called elementary if Φ = ∑m i=1 Mai,bi for some ai, bi ∈ A, i = 1, . . . ,m. Fong and Sourour showed that an elementary operator Φ : B(H) → B(H), where B(H) is the algebra of bounded linear operators on a Hilbert space H, is compact if and only if there exist compact operators ci, di ∈ B(H), i = 1, . . . ,m such that Φ = ∑m i=1 Mci,di [5]. This result was expanded by Mathieu on prime C*-algebras [9] and later on general C*-algebras by Timoney [14]. Akemann and Wright [1] characterized the weakly compact multiplication operators on B(H), where H is a Hilbert space. Saksman and Tylli [12, 13] and Johnson and Schechtman [6] studied weak compactness of multiplication operators in a Banach space setting. Moreover, strictly singular multiplication operators are studied by Lindström, Saksman and Tylli [8] and Mathieu and Tradacete [10]. Compactness properties of multiplication operators on nest algebras, a class of non selfadjoint operator algebras, are studied by Andreolas and Anoussis in [2]. In","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46054806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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