Quasi Centralizers and Inner Derivations in a Closed Ideal ‎of a Complex Banach Algebra

Quasi Centralizers and Inner Derivations in a Closed Ideal ‎of a Complex Banach Algebra

As'ad Y. As'ad

aasad@mail.iugaza.edu

Department of Mathematics, Faculty of Science, Islamic University, ‎Gaza, Palestine.‎

Received : 03-05-2003 , Accepted : 31-08-2004

Language: English

Abstract

In this paper we show that, for an ideal J of a unital complex Banach algebra A, we have (i) under certain conditions the ? -quasi centralizer, the quasi centralizer, and the centralizer of J are all identical, and so they are subsets of the ? -quasi centralizer of J. (ii) If J is closed and a is a quasi centralizer element of J, then DaJ, a restriction of the inner derivation of a to J is topologically nilpotent. (iii) For each complex number ? and each x in J we have, (? – a) x = 0 if and only if x (? – a) = 0.

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