International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 275-280
doi:10.1155/S0161171282000246
The compactum and finite dimensionality in Banach algebras
Abdullah H. Al-Moajil
Gulf Organization for Industrial Consulting, P.O. Box 5114, Doha, Qatar
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→xax 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.