On vector valued multipliers for the class of strongly HK-integrable functions

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] \to X is of bounded variation, then the multiplication operator defined by $Mg(f) := fg$ maps $\mathcal{SHK}$ to $\mathcal{HK}$. We also prove a partial converse, when $X$ is a Gel'fand space.