Vector Valued Multipliers of McShane Integrable Functions

Abstract

We study the algebra of vector valued multipliers of Banach algebra valued McShane integrable functions. We prove that if X is a commutative Banach algebra, with identity e of norm one, then functions associated with measures of strong bounded variation and the set {L?([a, b],?) e} are vector valued multipliers of McShane integrable functions. We find some necessary and another set of sufficient conditions for a functiong to define a multiplier. In case X satisfies Radon Nikodym property (weak Radon Nikodym property), we study multiplier operators.