The compactum of a semi-simple commutative Banach algebra

Abduliah H. Al-Moajil

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-2

Abstract:

Let A 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 S ( A ) (the socle of A ) denote this set. Let C ( A ) denote the set of elements x in A such that the map a → x a x is compact. It is shown that C ( A ) is the norm closure of S ( A ) .

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:483625

DOI: 10.1155/S0161171284000855

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