Equivalence of some properties in the theory of Banach algebras and applications

Abstract

In this work, we establish a sequential characterization of the notion of relatively weak compactness of Banach algebras introduced recently by J. Banaś and L. Olszowy. Moreover, we show that this structure is one of the most important properties which could be lifted from a Banach algebra X to C(K,X) and L1(μ,X). In addition, fixed point theorems for the product of two nonlinear operators acting on RWC-Banach algebra are proved by the help of the De Blasi measure of weak noncompactness.