Communications in Algebra· 2026Q2
The Bochner-Eberlein-Doss property for θ-Lau product of Banach algebras
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- 2026year
Short summary
Researchers establish that the θ-Lau product of two commutative Banach algebras, A×θB, is a Bochner-Eberlein-Doss (BED) algebra if and only if both Ae and B are BED algebras, provided A and B are non-unital and semisimple.
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Key points
- The BED property of the θ-Lau product A×θB is equivalent to the BED property of Ae and B for non-unital, semisimple commutative Banach algebras.
- The condition for A×θB to be without order is shown to be equivalent to B being without order.
- The findings extend existing results on θ-Lau products of Banach algebras.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let (A,∥⋅∥A) and (B,∥⋅∥B) be two commutative Banach algebras with nonempty character spaces and θ∈Δ(B). The aim of this paper is to verify the BED property for the θ-Lau product of A and B, denoted by A×θB, whenever A and B are non-unital and semisimple. First, along with all available results regarding θ-Lau product of Banach algebras, we prove that A×θB is without order if and only if B is so. Then as the main result of the present work, we establish that A×θB is a BED algebra if and only if Ae and B are so.
The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics