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

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

Fatemeh Abtahi, Ali Rejali, Farshad Sayaf   

  1. 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 BSE PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS*

Fatemeh Abtahi, Ali Rejali, Farshad Sayaf   

  1. 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: In this paper, X is a locally compact Hausdorff space and A is a Banach algebra. First, we study some basic features of C0(X,A) related to BSE concept, which are gotten from A. In particular, we prove that if C0(X,A) has the BSE property then A has so. We also establish the converse of this result, whenever X is discrete and A has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that C0(X,A) has the BSE-norm property if and only if A has so.

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

Abstract: In this paper, X is a locally compact Hausdorff space and A is a Banach algebra. First, we study some basic features of C0(X,A) related to BSE concept, which are gotten from A. In particular, we prove that if C0(X,A) has the BSE property then A has so. We also establish the converse of this result, whenever X is discrete and A has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that C0(X,A) has the BSE-norm property if and only if A has so.

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

中图分类号: 

  • 46J05