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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Vector measures with values in the compact operators


Author: Werner Ricker
Journal: Proc. Amer. Math. Soc. 102 (1988), 441-442
MSC: Primary 28B05,; Secondary 46G10,47B05
MathSciNet review: 921014
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Abstract: As a consequence of a recent result due to Kaftal and Wiess it is shown that any vector measure (for the strong operator topology) with values in the space of compact operators on a Hilbert space is $ \sigma $-additive for the uniform operator topology. This leads to an elegant and simple proof of a result due to Diestel and Faires on the uniform operator $ \sigma $-additivity of the indefinite integral induced by a compact selfadjoint operator.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0921014-3
Article copyright: © Copyright 1988 American Mathematical Society