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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 401-402
doi:10.1155/S0161171293000481

A generalization of Gelfand-Mazur theorem

Sung Guen Kim

Department of Mathematics, Pohang Institute of Science and Technology, P.O. Box 215, Pohang 790-600, Korea

Abstract

In this paper, we show that if A is a unital semisimple complex Banach algebra with only the trivial idempotents and if σA(x) is countable for each x∈Fr(G(A)), then A≅C, this generalizes the Gelfand-Mazur theorem.