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|Title||σ - Quasi Centralizers and Inner Derivations in a Closed Ideal of a Complex Banach Algebra.|
In this paper we show that, for a closed ideal J of a unital complex Banach algebra A and for a σ -quasi centralizer element a of J in A we have (i) under certain conditions if b is an element in the center of J and π : J → BL( X ) is an irreducible representation of J on the Banach space X , then π(ba) is a scalar operator. (ii) If σA(a) has empty interior and DaJ is the restriction of the inner derivation of a to J then ( DaJ )3 = 0.
|Published in||IUG Journal for Natural and Engineering Studies|
|Series||Volume: 16, Number: 1|
|Publisher||الجامعة الإسلامية - غزة|
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