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2019 The Radon Nikodym Property and Multipliers of \(\mathcal{HK}\)-Integrable Functions
Savita Bhatnagar
Real Anal. Exchange 44(2): 391-402 (2019). DOI: 10.14321/realanalexch.44.2.0391

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.

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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

Information

Published: 2019
First available in Project Euclid: 1 May 2020

zbMATH: 07211598
Digital Object Identifier: 10.14321/realanalexch.44.2.0391

Subjects:
Primary: 26A39
Secondary: 28B05

Rights: Copyright © 2019 Michigan State University Press

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Vol.44 • No. 2 • 2019
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