On power compact operators
Abstract: We give an operator theoretic proof of the following result of D. G. Tacon:
Theorem. If is a sequence of bounded linear operators in a complex infinite dimensional Hilbert space with the property that for every bounded sequence there exists a positive integer k such that the sequence has a convergent subsequence, then there exists k such that is a compact operator.
-  D. G. Tacon, Two characterizations of power compact operators, Proc. Amer. Math. Soc. 73 (1979), no. 3, 356–360. MR 518519, https://doi.org/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 0415338
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