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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On power compact operators


Author: José Barría
Journal: Proc. Amer. Math. Soc. 80 (1980), 123-124
MSC: Primary 47B05
MathSciNet review: 574520
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0574520-0
Keywords: Compact operator
Article copyright: © Copyright 1980 American Mathematical Society