THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS*

doi:10.1007/s10473-024-0518-z

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1945-1954.doi: 10.1007/s10473-024-0518-z

THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS^*

Fatemeh Abtahi, Ali Rejali^†, Farshad Sayaf

Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Iran

收稿日期:2022-10-21 修回日期:2023-09-24 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Ali Rejali, E-mail,: rejali@sci.ui.ac.ir;
作者简介:Fatemeh Abtahi,E-mail,: f.abtahi@sci.ui.ac.ir; Farshad Sayaf, E-mail,: f.sayaf@sci.ui.ac.ir

THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS^*

Fatemeh Abtahi, Ali Rejali^†, Farshad Sayaf

Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Iran

Received:2022-10-21 Revised:2023-09-24 Online:2024-10-25 Published:2024-10-22
Contact: †Ali Rejali, E-mail,: rejali@sci.ui.ac.ir;
About author:Fatemeh Abtahi,E-mail,: f.abtahi@sci.ui.ac.ir; Farshad Sayaf, E-mail,: f.sayaf@sci.ui.ac.ir

摘要/Abstract

摘要： In this paper, $X$ is a locally compact Hausdorff space and ${\mathcal A}$ is a Banach algebra. First, we study some basic features of $C_0(X,\mathcal A)$ related to $\rm BSE$ concept, which are gotten from ${\mathcal A}$. In particular, we prove that if $C_0(X,\mathcal A)$ has the $\rm BSE$ property then $\mathcal A$ has so. We also establish the converse of this result, whenever $X$ is discrete and $\mathcal A$ has the BSE-norm property. Furthermore, we prove the same result for the $\rm BSE$ property of type I. Finally, we prove that $C_0(X,{\mathcal A})$ has the BSE-norm property if and only if $\mathcal A$ has so.

关键词: $\rm BSE $ algebras, $\rm BSE $-function, $\rm BSE $ norm, multiplier algebra, semisimple, without order

Abstract: In this paper, $X$ is a locally compact Hausdorff space and ${\mathcal A}$ is a Banach algebra. First, we study some basic features of $C_0(X,\mathcal A)$ related to $\rm BSE$ concept, which are gotten from ${\mathcal A}$. In particular, we prove that if $C_0(X,\mathcal A)$ has the $\rm BSE$ property then $\mathcal A$ has so. We also establish the converse of this result, whenever $X$ is discrete and $\mathcal A$ has the BSE-norm property. Furthermore, we prove the same result for the $\rm BSE$ property of type I. Finally, we prove that $C_0(X,{\mathcal A})$ has the BSE-norm property if and only if $\mathcal A$ has so.

Key words: $\rm BSE $ algebras, $\rm BSE $-function, $\rm BSE $ norm, multiplier algebra, semisimple, without order

中图分类号:

46J05

Fatemeh Abtahi, Ali Rejali, Farshad Sayaf. THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS^*[J]. 数学物理学报(英文版), 2024, 44(5): 1945-1954.

Fatemeh Abtahi, Ali Rejali, Farshad Sayaf. THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1945-1954.

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THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS^*

THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS^*

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