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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weakly constricted operators and Jamison's convergence theorem


Author: Robert Sine
Journal: Proc. Amer. Math. Soc. 106 (1989), 751-755
MSC: Primary 47B38; Secondary 47A35, 47D05
MathSciNet review: 965945
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Abstract: If $ T$ is a linear contraction on a complex $ C(X)$ space which is irreducible and if $ \{ {T^n}f\} $ converges weakly to zero then the convergence is actually in norm. If $ T$ is weakly constricted and irreducible then $ T$ is actually strongly constricted. If $ T$ is weakly almost periodic and irreducible and either $ T$ or $ {T^*}$ has a unimodular point spectral value then $ T$ is strongly almost periodic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0965945-8
PII: S 0002-9939(1989)0965945-8
Keywords: Markov operator, almost periodic operator, deLeeuw-Glicksberg decomposition, constricted operator
Article copyright: © Copyright 1989 American Mathematical Society