The multiplier algebra and BSE-functions for certain product of Banach algebras
Mehdi Nemati, Hossein Javanshiri

TL;DR
This paper characterizes the multiplier algebra and BSE-functions for certain product Banach algebras, providing new insights into their structure and properties, especially for semidirect and Lau product algebras.
Contribution
It offers a novel characterization of the multiplier algebra of semidirect product Banach algebras and describes BSE-functions for their Lau products, advancing understanding of their algebraic and functional properties.
Findings
Multiplier algebra of semidirect product algebra characterized
BSE-property of these Banach algebras investigated
BSE-functions on Lau product characterized in terms of component algebras
Abstract
In this paper, we characterize the (left) multiplier algebra of a semidirect product algebra , where and are closed two-sided ideal and closed subalgebra of , respectively. As an application of this result we investigate the BSE-property of this class of Banach algebras. We then for two commutative semisimple Banach algebras and characterize the BSE-functions on the carrier space of , the -Lau product of and , in terms of those functions on carrier spaces of and . We also prove that is a BSE-algebra if and only if both and are BSE.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Holomorphic and Operator Theory
