{"title":"On a characterization of Jeribi, Rakočević, Schechter, Schmoeger and Wolf essential spectra of a 3⨉3 block operator matrices with non diagonal domain and application","authors":"N. Moalla, W. Selmi","doi":"10.7153/oam-2022-16-12","DOIUrl":"https://doi.org/10.7153/oam-2022-16-12","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222865","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}
. In this paper, we consider a periodic quantum graph corresponding to graphene with a variant of the zigzag shape of boundaries. The aim of this paper is to compare the spectra of our graphs with the spectra of quantum graphs with the standard zigzag boundaries. For this purpose, we utilize a Shnol type theorem and the Cramer’s rule to construct two spectral discriminants D s ( μ , λ ) and D c ( μ , λ ) , where μ = S 1 : = [ − π , π ) is a quasi-momentum of a corresponding fi ber operator and λ ∈ R is a spectral parameter. As a result, we derive pictures of a part of the dispersion relation for our quantum graph.
． 在本文中，我们考虑了一个与石墨烯相对应的周期量子图，其边界是锯齿形的变体。本文的目的是将我们图的谱与具有标准之字形边界的量子图的谱进行比较。为此，我们利用Shnol型定理和Cramer规则构造了两个谱判据D s (μ， λ)和D c (μ， λ)，其中μ = s1: =[−π， π)是对应光纤算子的拟动量，λ∈R是谱参数。因此，我们得到了量子图色散关系的一部分图像。
{"title":"Spectra of graphenes with variant edges","authors":"Hiroaki Niikuni","doi":"10.7153/oam-2022-16-71","DOIUrl":"https://doi.org/10.7153/oam-2022-16-71","url":null,"abstract":". In this paper, we consider a periodic quantum graph corresponding to graphene with a variant of the zigzag shape of boundaries. The aim of this paper is to compare the spectra of our graphs with the spectra of quantum graphs with the standard zigzag boundaries. For this purpose, we utilize a Shnol type theorem and the Cramer’s rule to construct two spectral discriminants D s ( μ , λ ) and D c ( μ , λ ) , where μ = S 1 : = [ − π , π ) is a quasi-momentum of a corresponding fi ber operator and λ ∈ R is a spectral parameter. As a result, we derive pictures of a part of the dispersion relation for our quantum graph.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71223955","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}
{"title":"Numerical radii of weighted shift operators using determinantal polynomials","authors":"Bikshan Chakraborty, Sarita Ojha, R. Birbonshi","doi":"10.7153/oam-2022-16-75","DOIUrl":"https://doi.org/10.7153/oam-2022-16-75","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71224071","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}
. This paper is focused on Jensen’s inequality and its variants. Various refinements and reverses of Jensen’s inequality, including scalar and operator versions, are given.
{"title":"Refining and reversing Jensen's inequality","authors":"Leila Nasiri, A. Zardadi, H. Moradi","doi":"10.7153/oam-2022-16-03","DOIUrl":"https://doi.org/10.7153/oam-2022-16-03","url":null,"abstract":". This paper is focused on Jensen’s inequality and its variants. Various refinements and reverses of Jensen’s inequality, including scalar and operator versions, are given.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222525","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}
{"title":"Generalization of Wolff's ideal theorem on H_K(B)^∞(ᵓb)","authors":"D. Banjade, M. Ephrem","doi":"10.7153/oam-2022-16-13","DOIUrl":"https://doi.org/10.7153/oam-2022-16-13","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222882","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}
{"title":"Singular value structure of real matrices which can be expressed as a linear combination of two orthogonal matrices","authors":"Zhenyu Li, Tie Zhang, Chang-Jun Li","doi":"10.7153/oam-2022-16-55","DOIUrl":"https://doi.org/10.7153/oam-2022-16-55","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71223983","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}
. We study a speci fi c family of symmetric norms on the algebra B ( H ) of operators on a separable in fi nite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain its norm. Using this, we generalize one of the main results from [8]; the hypothesis is relaxed, and consequently, the family of symmetric norms for which the result holds is extended. We introduce and study the concepts of “universally symmetric norming operators” and “universally absolutely symmetric norming operators” on a separable Hilbert space. These refer to the operators that are, respectively, norming and absolutely norming, with respect to every symmetric norm on B ( H ) . We establish a characterization theorem for such operators and prove that these classes are identical, and that they coincide with the class of compact operators. In particular, we provide an alternative characterization of compact operators on a separable in fi nite-dimensional Hilbert space.
{"title":"Universally symmetric norming operators are compact","authors":"S. Pandey","doi":"10.7153/oam-2022-16-63","DOIUrl":"https://doi.org/10.7153/oam-2022-16-63","url":null,"abstract":". We study a speci fi c family of symmetric norms on the algebra B ( H ) of operators on a separable in fi nite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain its norm. Using this, we generalize one of the main results from [8]; the hypothesis is relaxed, and consequently, the family of symmetric norms for which the result holds is extended. We introduce and study the concepts of “universally symmetric norming operators” and “universally absolutely symmetric norming operators” on a separable Hilbert space. These refer to the operators that are, respectively, norming and absolutely norming, with respect to every symmetric norm on B ( H ) . We establish a characterization theorem for such operators and prove that these classes are identical, and that they coincide with the class of compact operators. In particular, we provide an alternative characterization of compact operators on a separable in fi nite-dimensional Hilbert space.","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71224293","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}
. Let K denotes the field of real or complex numbers. For a locally compact Hausdorff space X , we denote by C 0 ( X ) the space of all K -valued continuous functions on X vanishing at infinity. Let E be a (real or complex) Banach space, K E be a closed subset of E , and C u ( K E ) be the algebra of all real or complex valued, uniformly continuous bounded functions defined on K E . Endowed with the supremum norm, both C 0 ( X ) and C u ( K E ) are Banach spaces. In this paper we study the structure of local isometries on subspaces of C 0 ( X ) and various subalgebras of C u ( K E ) .
{"title":"Local isometries on subspaces and subalgebras of function spaces","authors":"Abdullah Bin Abu Baker, Rahul Maurya","doi":"10.7153/oam-2022-16-02","DOIUrl":"https://doi.org/10.7153/oam-2022-16-02","url":null,"abstract":". Let K denotes the field of real or complex numbers. For a locally compact Hausdorff space X , we denote by C 0 ( X ) the space of all K -valued continuous functions on X vanishing at infinity. Let E be a (real or complex) Banach space, K E be a closed subset of E , and C u ( K E ) be the algebra of all real or complex valued, uniformly continuous bounded functions defined on K E . Endowed with the supremum norm, both C 0 ( X ) and C u ( K E ) are Banach spaces. In this paper we study the structure of local isometries on subspaces of C 0 ( X ) and various subalgebras of C u ( K E ) .","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222480","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}
{"title":"Distinguished subspaces of Topelitz operators on N_ɸ-type quotient modules","authors":"Hong Zou, Tao Yu","doi":"10.7153/oam-2022-16-22","DOIUrl":"https://doi.org/10.7153/oam-2022-16-22","url":null,"abstract":"","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71222946","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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