Space of Operators and Property (<i>MB</i>)

Abstract

In this paper, a new class of Banach spaces, termed as Banach spaces with property ( MB ) , will be introduced. It is stated that a space X has property ( MB ) if every V -subset of X* is an L -subset of X* . We describe those spaces which have property ( MB ) . Also, we show that if a Banach space X has property ( MB ) and Banach space Y does not contain , then every operator is completely continuous.