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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 519-522
doi:10.1155/S0161171284000570

Finite dimensionality in socle of Banach algebras

Sin-Ei Takahasi

Department of Mathematics, Ibaraki University, Mito, Ibaraki 310, Japan

Abstract

It is shown that if the socle soc(A) of a semisimple Banach algebra A is norm-closed, then soc(A) is already finite dimensional. The proof makes use of the Al-Moajil theorem. However it is remarked that our main theorem is an extension of the Al-Moajil's.