<abstract xmlns="http://www.w3.org/1999/xhtml">We investigate the space of vector valued multipliers of strongly Henstock-Kurzweil integrable functions. We prove that if <italic>X</italic> is a commutative Banach algebra with identity <italic>e</italic> such that ‖<italic>e</italic>‖ = 1 and <italic>g</italic> : [<italic>a</italic>, <italic>b</italic>] → <italic>X</italic> is of strongly bounded variation, then the multiplication operator defined by <italic>Mg</italic>(<italic>f</italic>) := <italic>fg</italic> maps 𝒮ℋ𝒦 to ℋ𝒦. We also prove a partial converse, when <italic>X</italic> is a Gel’fand space.</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 Mg(f) := fg maps 𝒮ℋ𝒦 to ℋ𝒦. We also prove a partial converse, when X is a Gel’fand space.

On Vector Valued Multipliers for the Class of Strongly <italic>ℋ𝒦</italic>-Integrable Functions

Center for Advanced Study in Mathematics, Department of Mathematics

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

We investigate the space of vector valued multipliers of strongly Henstock-Kurzweil integrable functions. We prove that if X is a commutative Banach algebra...

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

Published Online: Nov 18, 2017

Page range: 69 - 79

Received: Oct 24, 2016

DOI: https://doi.org/10.1515/tmmp-2017-0006

Keywords
strong Henstock-Kurzweil integrability, bounded variation, Banach algebra, multiplier, * functions, Radon-Nikodym property

© 2017 Surinder Pal Singh et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Nov 18, 2017

Page range: 69 - 79

Received: Oct 24, 2016

DOI: https://doi.org/10.1515/tmmp-2017-0006

Keywordsstrong Henstock-Kurzweil integrability, bounded variation, Banach algebra, multiplier, * functions, Radon-Nikodym property

© 2017 Surinder Pal Singh et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
strong Henstock-Kurzweil integrability, bounded variation, Banach algebra, multiplier, * functions, Radon-Nikodym property