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The compactum and finite dimensionality in Banach algebras

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  • Abdullah H. Al-Moajil

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 .

Suggested Citation

  • Abdullah H. Al-Moajil, 1982. "The compactum and finite dimensionality in Banach algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 5, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:807919
    DOI: 10.1155/S0161171282000246
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