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Mat. Zametki, 2002, Volume 71, Issue 5, Pages 725–731 (Mi mz380)  

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.

DOI: https://doi.org/10.4213/mzm380

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

Bibliographic databases:

UDC: 517.98
Received: 08.09.1999
Revised: 10.10.2001

Citation: H. S. Mustafaev, “Banach Algebras with Bounded Groups of Generators, and the Schur Property”, Mat. Zametki, 71:5 (2002), 725–731; Math. Notes, 71:5 (2002), 661–666

Citation in format AMSBIB
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