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
Department of Mathematics, Pohang Institute of Science and Technology, P.O. Box 215, Pohang 790-600, Korea
Received 12 August 1991; Revised 19 November 1991
Copyright © 1993 Sung Guen Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.