The compactum of a semi-simple commutative Banach algebra

International Journal of Mathematics and Mathematical Sciences

Abduliah H. Al-Moajil¹ 

[1] Gulf Organization For Industrial Consulting, P. O. Box 5114, Doha, Qatar;

关键词: commutative Banach algebra;    semi-simple;    socle;    compactum;    spectrum;    carrier space;    idempotent.;   

DOI  :  10.1155/S0161171284000855

来源: DOAJ

【 摘 要 】

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→xax is compact. It is shown that C(A) is the norm closure of S(A).

【 授权许可】

Unknown