Abstract
We study the space of vector valued multipliers of strongly Henstock-Kurzweil \((\mathcal{SHK})\) integrable functions. We prove that if \(X\) is a commutative Banach algebra, with identity \(e\) of norm one, satisfying Radon-Nikodym property and \(g:[a,b] \rightarrow X\) is of strong bounded variation, then the multiplication operator defined by \(M_g(f)=fg\) maps \(\mathcal{SHK}\) to \(\mathcal{SHK}.\) We also investigate the problems when the domain is \(\mathcal{HK}\) or when \(X\) satisfies weak Radon-Nikodym property.
Citation
Savita Bhatnagar. "The Radon Nikodym Property and Multipliers of \(\mathcal{HK}\)-Integrable Functions." Real Anal. Exchange 44 (2) 391 - 402, 2019. https://doi.org/10.14321/realanalexch.44.2.0391
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