The compactum and finite dimensionality in Banach algebras

Abdullah H. Al-Moajil

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-6

Abstract:

Given a Banach algebra A , the compactum of A is defined to be the set of elements x ∈ A such that the operator a → x a x is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in terms of the compactum and the socle of A .

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:807919

DOI: 10.1155/S0161171282000246

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