TITLE:
Space of Operators and Property (MB)
AUTHORS:
Manijeh Esfahani Bahreini
KEYWORDS:
L-Sets, V -Sets, Completely Continuous Operators, Unconditionally Converging Operators
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.13,
December
15,
2016
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.