The Socle and Finite Dimensionality of some Banach Algebras

Proceedings Mathematical Sciences

Ali Reza Medghalchi¹  Ali Ghaffari² 

[1] $$;Department of Mathematics, Semnan University, Semnan, Iran$$

关键词: Banach algebras;    Socle;    finite dimensional;    locally compact group.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group 𝐺, 𝐺 is compact if there exists a measure 𝜇 in $mathrm{Soc} (L^1(G))$ such that 𝜇(𝐺) ≠ 0. We also prove that 𝐺 is finite if $mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in 𝑀(𝐺) contains a minimal left ideal.

【 授权许可】

Unknown