On vector valued multipliers for the class of strongly $\mahcal{HK}$-integrable functions

Year, pages: 2017, 69 - 79

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 $\norm e \norm = 1$ and $g\colon [a,b]\longrightarrow X$ is of strongly bounded variation, then the multiplication operator defined by $M_g(f):=fg$ maps $\mathcal{SHK}$ to $\mathcal{HK}$. We also prove a partial converse, when $X$ is a Gel'fand space.

Singh, S., Bhatnagar, S. 2017. On vector valued multipliers for the class of strongly $\mahcal{HK}$-integrable functions. In Tatra Mountains Mathematical Publications, vol. 68, no.1, pp. 69-79. 1210-3195.

Singh, S., Bhatnagar, S. (2017). On vector valued multipliers for the class of strongly $\mahcal{HK}$-integrable functions. Tatra Mountains Mathematical Publications, 68(1), 69-79. 1210-3195.