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

H. S. Mustafaev

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

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.

UDC: 517.98

Received: 08.09.1999
Revised: 10.10.2001

DOI: 10.4213/mzm380

 English version: Mathematical Notes, 2002, 71:5, 661–666

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