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

Surinder Pal Singh; Savita Bhatnagar

doi:10.1515/tmmp-2017-0006

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

Tatra Mountains Mathematical Publications

Volume 68 (2017): Issue 1 (March 2017)

By: Surinder Pal Singh and Savita Bhatnagar

Open Access

|Nov 2017

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 M_g(f) := f_g maps 𝒮ℋ𝒦 to ℋ𝒦. We also prove a partial converse, when X is a Gel’fand space.

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Articles in this issue

DOI: https://doi.org/10.1515/tmmp-2017-0006 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 69 - 79

Submitted on: Oct 24, 2016

Published on: Nov 18, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

strong Henstock-Kurzweil integrability,

Radon-Nikodym property

Related subjects:

Mathematics,

General mathematics

© 2017 Surinder Pal Singh, Savita Bhatnagar, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 68 (2017): Issue 1 (March 2017)