Vector measures with values in the compact operators
HTML articles powered by AMS MathViewer
- by Werner Ricker
- Proc. Amer. Math. Soc. 102 (1988), 441-442
- DOI: https://doi.org/10.1090/S0002-9939-1988-0921014-3
- PDF | 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
- J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc. 198 (1974), 253–271. MR 350420, DOI 10.1090/S0002-9947-1974-0350420-8
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
- Victor Kaftal and Gary Weiss, A Riemann type theorem for unconditional convergence of operators, Proc. Amer. Math. Soc. 98 (1986), no. 3, 431–435. MR 857935, DOI 10.1090/S0002-9939-1986-0857935-8
- Alan Shuchat, Infrabarreled spaces, linear operators and vector measures, Bull. Soc. Roy. Sci. Liège 48 (1979), no. 5-8, 153–157. MR 556242
Similar Articles
- Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28B05,, 46G10,47B05
- Retrieve articles in all journals with MSC: 28B05,, 46G10,47B05
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- 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