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A class of banach algebras whose duals have the schur property

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Mustafayev, Heybetkulu

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Call a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).

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Scientific and Technical research Council of Turkey - TUBITAK/Türkiye Bilimsel ve Teknik Araştırma Kurumu

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Mathematics

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Turkish Journal of Mathematics

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