A NOTE ON STRONGLY FULLY STABLE BANACH ALGEBRA MODULES RELATIVE TO AN IDEAL

Abstract

Let A be a unital algebra, a Banach algebra module M is strongly fully stable Banach A-module relative to ideal K of A, if for every submodule N of M and for each multiplier θ : N \(\longrightarrow\) M such that θ(N ) ⊆ N ∩ KM.  In this paper, we adopt the concept of strongly fully stable Banach Algebra modules relative to an ideal which generalizes that of fully stable Banach Algebra modules and we study the properties and characterizations of strongly fully stable Banach A-module relative to ideal K of A.