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May 2018 Spectral properties of the Lau product A×θB of Banach algebras
Prakash A. Dabhi, Savan K. Patel
Ann. Funct. Anal. 9(2): 246-257 (May 2018). DOI: 10.1215/20088752-2017-0048

Abstract

Let A and B be commutative Banach algebras. Then a multiplicative linear functional θ on B induces a multiplication on the Cartesian product space A×B given by (a,b)(c,d)=(ac+θ(d)a+θ(b)c,bd) for all (a,b),(c,d)A×B. We show that this Lau product is stable with respect to the spectral properties like the unique uniform norm property, the spectral extension property, the multiplicative Hahn–Banach property, and the unique semisimple norm property under certain conditions on θ.

Citation

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Prakash A. Dabhi. Savan K. Patel. "Spectral properties of the Lau product A×θB of Banach algebras." Ann. Funct. Anal. 9 (2) 246 - 257, May 2018. https://doi.org/10.1215/20088752-2017-0048

Information

Received: 7 March 2017; Accepted: 31 May 2017; Published: May 2018
First available in Project Euclid: 7 December 2017

zbMATH: 06873701
MathSciNet: MR3795089
Digital Object Identifier: 10.1215/20088752-2017-0048

Subjects:
Primary: 46J05
Secondary: 46Jxx

Keywords: commutative Banach algebra , Gelfand space , multiplicative Hahn–Banach property , Shilov boundary , spectral extension property , unique uniform norm property

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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