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

 

A Riemann type theorem for unconditional convergence of operators


Authors: Victor Kaftal and Gary Weiss
Journal: Proc. Amer. Math. Soc. 98 (1986), 431-435
MSC: Primary 47B05; Secondary 47A05
MathSciNet review: 857935
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Abstract: We prove that if a series of bounded linear operators is compactly conditionally convergent in the strong operator topology, that is, each of its partial sums converge, in the strong operator topology to a compact operator, then the series converges in the uniform (operator norm) topology; although not necessarily absolutely. In case the operators are all mutually diagonalizable, then under the same hypothesis, the series converges absolutely uniformly.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857935-8
PII: S 0002-9939(1986)0857935-8
Article copyright: © Copyright 1986 American Mathematical Society