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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
DOI: https://doi.org/10.1090/S0002-9939-1988-0921014-3
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.


References [Enhancements On Off] (What's this?)

  • [1] J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc. 198 (1974), 253-271. MR 0350420 (50:2912)
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  • [3] V. Kaftal and G. Wiess, A Riemann type theorem for unconditional convergence of operators, Proc. Amer. Math. Soc. 98 (1986), 431-435. MR 857935 (87j:47029)
  • [4] A. Shuchat, Infrabarreled spaces, linear operators and vector measures, Bull. Soc. Roy. Sci. Liège 48 (1979), 153-157. MR 556242 (81d:46002)

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

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