A Riemann type theorem for unconditional convergence of operators
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- by Victor Kaftal and Gary Weiss PDF
- Proc. Amer. Math. Soc. 98 (1986), 431-435 Request permission
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.References
- J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. 10-I, Academic Press, New York-London, 1969. Enlarged and corrected printing. MR 0349288
- Victor Kaftal and Gary Weiss, Compact derivations relative to semifinite von Neumann algebras, J. Funct. Anal. 62 (1985), no. 2, 202–220. MR 791847, DOI 10.1016/0022-1236(85)90003-5
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Walter Rudin, Principles of mathematical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0055409
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 431-435
- MSC: Primary 47B05; Secondary 47A05
- DOI: https://doi.org/10.1090/S0002-9939-1986-0857935-8
- MathSciNet review: 857935