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Banach Algebras with Bounded Groups of Generators, and the Schur Property

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Abstract

Recall that a Banach space X is said to have the Schur property if any weakly compact set in X is strongly compact. In this note we consider a Banach algebra A that has a bounded group of generators. Along with other results, it is proved that if \(A^*\) has the Schur property, then the Gelfand space of the algebra A is a scattered set and, moreover, \(A^*\) has the Radon--Nikodym property.

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  1. Institute of Mathematics and Mechanics, Azerbaijan Academy of Sciences, Baku

    G. S. Mustafaev

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  1. G. S. Mustafaev
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Mustafaev, G.S. Banach Algebras with Bounded Groups of Generators, and the Schur Property. Mathematical Notes 71, 661–666 (2002). https://doi.org/10.1023/A:1015887921585

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