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)

 

 

Two characterizations of power compact operators


Author: D. G. Tacon
Journal: Proc. Amer. Math. Soc. 73 (1979), 356-360
MSC: Primary 47B05; Secondary 03H05
DOI: https://doi.org/10.1090/S0002-9939-1979-0518519-0
MathSciNet review: 518519
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if T is an operator on a Banach space with the property that for every bounded sequence $ \{ {x_n}\} $ there is an integer k such that $ \{ {T^k}({x_n})\} $ has a convergent subsequence then T is power compact. The equivalent nonstandard characterization is that for each finite point p in an $ {\aleph _1}$-saturated enlargement of the space there is an integer k such that $ {T^k}p$ is near-standard. Similar results are shown to hold for countable families of operators and for operators possessing weakly compact powers.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B05, 03H05

Retrieve articles in all journals with MSC: 47B05, 03H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0518519-0
Keywords: Banach space, operator, compact, weakly compact, $ {\aleph _1}$-saturated enlargement, nonstandard analysis
Article copyright: © Copyright 1979 American Mathematical Society