We show that the Banach $\mathcal{A}\rtimes\mathfrak{A}$-module $X\times Y$ ($X$ is a Banach $\mathcal{A},\mathfrak{A}$-module and $Y$ is a Banach $\mathfrak{A}$-module) has a BSE-module property if and only if $X$ is a BSE Banach $\mathcal{A},\mathfrak{A}$-module and $Y$ is a BSE Banach $\mathfrak{A}$-module.
📌 3 Key Takeaways
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Objective & Hypothesis:The Bochner-Schoenberg-Eberlein module property on commutative Banach algebras is a property related to extensions of multipliers on Banach algebras to module morphisms from Banach algebras into Banach modules.
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Key Findings & Data:In this paper, we answer the problem (1) raised in [J.
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Conclusion & Impact:We show that the Banach $\mathcal{A}\rtimes\mathfrak{A}$-module $X\times Y$ ($X$ is a Banach $\mathcal{A},\mathfrak{A}$-module and $Y$ is a Banach $\mathfrak{A}$-module) has a BSE-module property if and only if $X$ is a BSE Banach $\mathcal{A},\mathfrak{A}$-module and $Y$ is a BSE Banach $\mathfrak{A}$-module.
The Bochner-Schoenberg-Eberlein module property on commutative Banach algebras is a property related to extensions of multipliers on Banach algebras to module morphisms from Banach algebras into Banach modules. In this paper, we answer the problem (1) raised in [J. Algebra Appl., 21(8) (2022), 2250155, DOI: 10.1142/S0219498822501559]. We show that the Banach $\mathcal{A}\rtimes\mathfrak{A}$-module $X\times Y$ ($X$ is a Banach $\mathcal{A},\mathfrak{A}$-module and $Y$ is a Banach $\mathfrak{A}$-module) has a BSE-module property if and only if $X$ is a BSE Banach $\mathcal{A},\mathfrak{A}$-module and $Y$ is a BSE Banach $\mathfrak{A}$-module.
Abolfathi, M. A., Ebadian, A., Jabbari, A. (2024). The Bochner-Schoenberg-Eberlein module property for amalgamated duplication of Banach algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 4. https://doi.org/10.15672/hujms.1261110
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