International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 519-522

Finite dimensionality in scole of Banach algebras

Sin-Ei Takahasi

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

Received 23 September 1982

Copyright © 1984 Sin-Ei Takahasi. 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.


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.