On power compact operators
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- by José Barría PDF
- Proc. Amer. Math. Soc. 80 (1980), 123-124 Request permission
Abstract:
We give an operator theoretic proof of the following result of D. G. Tacon: Theorem. If $\{ {T_n}\}$ is a sequence of bounded linear operators in a complex infinite dimensional Hilbert space with the property that for every bounded sequence $\{ {x_n}\}$ there exists a positive integer k such that the sequence $\{ {T_k}{x_n}\} _{n = 1}^\infty$ has a convergent subsequence, then there exists k such that ${T_k}$ is a compact operator.References
- D. G. Tacon, Two characterizations of power compact operators, Proc. Amer. Math. Soc. 73 (1979), no. 3, 356–360. MR 518519, DOI 10.1090/S0002-9939-1979-0518519-0
- Dan Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), no. 1, 97–113. MR 415338
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 123-124
- MSC: Primary 47B05
- DOI: https://doi.org/10.1090/S0002-9939-1980-0574520-0
- MathSciNet review: 574520