A class of banach algebras whose duals have the schur property

Department of Mathematics2024-11-0919991300-0098N/A2-s2.0-0141846327N/Ahttps://hdl.handle.net/20.500.14288/8638Call 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).MathematicsA class of banach algebras whose duals have the schur propertyJournal Articlehttps://www.scopus.com/inward/record.uri?eid=2-s2.0-0141846327andpartnerID=40andmd5=9fcb7921dbd25f79b09856310088f160Q28786