Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] D. G. Tacon, Two characterizations of power compact operators, Proc. Amer. Math. Soc. 73 (1979), 356-360. MR 518519 (80d:47031)
  • [2] D. Voiculescu, A noncommutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97-113. MR 0415338 (54:3427)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B05

Retrieve articles in all journals with MSC: 47B05

Additional Information

Keywords: Compact operator
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society