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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Then, for a $gamma$-algebra A, we prove that $A^star$ has the Schur property iff the Gelfand spectrum $sum$ of A is scattered if $A^star$=ap(A) iff $A^star=overline{Span(sum)}$.
📌 3 Key Takeaways
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Objective & Hypothesis:Call a commutative Banach algebra A a $gamma$-algebra if it contains a bounded group $Gamma$ such that $overline{aco(Gamma)}$ contains a multiple of the unit ball of A.
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Key Findings & Data:In this paper, first by exhibiting several concrete examples, we show that the class of $gamma$-algebras is quite rich.
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Conclusion & Impact:Then, for a $gamma$-algebra A, we prove that $A^star$ has the Schur property iff the Gelfand spectrum $sum$ of A is scattered if $A^star$=ap(A) iff $A^star=overline{Span(sum)}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Call a commutative Banach algebra A a $gamma$-algebra if it contains a bounded group $Gamma$ such that $overline{aco(Gamma)}$ contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of $gamma$-algebras is quite rich. Then, for a $gamma$-algebra A, we prove that $A^star$ has the Schur property iff the Gelfand spectrum $sum$ of A is scattered if $A^star$=ap(A) iff $A^star=overline{Span(sum)}$.
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Cite This Article
MUSTAFAYEV, H., ÜLGER, A. (2022). A class of Banach algebras whose duals have the Schur propertry. Turkish Journal of Mathematics, Cilt: 23 - Sayı: 3, 441–452. https://ajindex.com/articles/608955