On Vector Valued Multipliers for the Class of Strongly ℋ𝒦-Integrable Functions

Abstract

Abstract We investigate the space of vector valued multipliers of strongly Henstock-Kurzweil integrable functions. We prove that if X is a commutative Banach algebra with identity e such that ‖e‖ = 1 and g : [a, b] → X is of strongly bounded variation, then the multiplication operator defined by Mg (f) := fg maps 𝒮ℋ𝒦 to ℋ𝒦. We also prove a partial converse, when X is a Gel’fand space.