International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 821-822
The compactum of a semi-simple commutative Banach algebra
Gulf Organization For Industrial Consulting, P. O. Box 5114, Doha, Qatar
Received 18 May 1983
Copyright © 1984 Abduliah H. Al-Moajil. 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.
Let be a commutative semi-simple Banach algebra such that the set consisting of finite sums of elements from minimal left ideals coincides with that of finite sums of elements from minimal right ideals. Let (the socle of ) denote this set. Let denote the set of elements in such that the map is compact. It is shown that is the norm closure of .