Conditions Which Imply a Banach Algebra is Finite Dimensional

IF 1.4 4区综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES

Iranian Journal of Science and Technology, Transactions A: Science Pub Date : 2024-06-25 DOI:10.1007/s40995-024-01662-4

G. H. Esslamzadeh, A. sahami, F. Taleghani

引用次数: 0

Abstract

It is a long standing conjecture that every contractible Banach algebra is finite dimensional. Motivated by this problem, we provide a survey of results in which certain conditions force a Banach algebra to be finite dimensional, with shorter proofs for a couple of them. These conditions are collected in three main groups: algebraic conditions, bounded cohomology contions and functional analytic ones.

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意味着巴拿赫代数是有限维的条件

一个长期存在的猜想是，每个可收缩的巴拿赫代数都是有限维的。受这一问题的启发，我们对某些条件迫使巴拿赫代数是有限维的结果进行了调查，并对其中几个进行了简短的证明。这些条件主要分为三组：代数条件、有界同调条件和函数解析条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Iranian Journal of Science and Technology, Transactions A: Science MULTIDISCIPLINARY SCIENCES-

CiteScore

4.00

自引率

5.90%

发文量

122

审稿时长

>12 weeks

期刊介绍： The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences