The BSE property for some vector-valued Banach function algebras

IF 1.2 4区 数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0518-z
Fatemeh Abtahi, Ali Rejali, Farshad Sayaf
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Abstract

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

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某些向量值巴拿赫函数代数的 BSE 特性
在本文中,X 是局部紧凑的 Hausdorff 空间,\({\cal A}\) 是一个巴拿赫代数。首先,我们研究了 C0(X, \({\cal A}\)) 与 BSE 概念相关的一些基本特征,这些特征是从 \({\cal A}\) 中得到的。特别是,我们证明如果 C0(X, \({\cal A}\)) 具有 BSE 属性,那么 \({\cal A}\) 也具有 BSE 属性。只要 X 是离散的,并且 \({\cal A}\) 具有 BSE 规范属性,我们也会建立这个结果的反面。最后,我们证明当且仅当\({\cal A}\)具有BSE-norm性质时,C0 (X, \({\cal A}\))才具有BSE-norm性质。
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来源期刊
CiteScore
2.00
自引率
10.00%
发文量
2614
审稿时长
6 months
期刊介绍: Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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