Vector measures with values in the compact operators

Ricker, Werner

doi:10.1090/S0002-9939-1988-0921014-3

Vector measures with values in the compact operators
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by Werner Ricker PDF

Proc. Amer. Math. Soc. 102 (1988), 441-442 Request permission

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

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