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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weakly compact groups of operators


Authors: T. A. Gillespie and T. T. West
Journal: Proc. Amer. Math. Soc. 49 (1975), 78-82
MSC: Primary 47D10
MathSciNet review: 0361924
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Abstract: It is shown that the weakly closed algebra generated by a weakly compact group of operators on a Banach space is reflexive and equals its second commutant. Also, an example is given to show that the generator of a monothetic weakly compact group of operators need not have a logarithm in the algebra of all bounded linear operators on the underlying space.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0361924-2
PII: S 0002-9939(1975)0361924-2
Article copyright: © Copyright 1975 American Mathematical Society