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Conditions Which Imply a Banach Algebra is Finite Dimensional

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Shiraz University, 71467-13565, Shiraz, Iran

    G. H. Esslamzadeh

  2. Department of Mathematics, Ilam University, Ilam, Iran

    A. sahami

  3. Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    F. Taleghani

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  1. G. H. Esslamzadeh
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  2. A. sahami
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  3. F. Taleghani
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Correspondence to G. H. Esslamzadeh.

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Esslamzadeh, G.H., sahami, A. & Taleghani, F. Conditions Which Imply a Banach Algebra is Finite Dimensional. Iran J Sci (2024). https://doi.org/10.1007/s40995-024-01662-4

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