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Proceedings of the American Mathematical Society

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

 

 

The iterates of a contraction and its adjoint


Author: John A. R. Holbrook
Journal: Proc. Amer. Math. Soc. 29 (1971), 543-546
MSC: Primary 47.10
DOI: https://doi.org/10.1090/S0002-9939-1971-0279606-0
MathSciNet review: 0279606
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Abstract: We prove that when T is a contraction on Hilbert space the size of $ \vert({({T^\ast})^n}h,g)\vert$ is controlled by that of $ \lim \sup \vert({T^n}h,g)\vert$. We give an application to Fourier-Stieltjes coefficients. Important in the proof is a generalization of the technique of orthogonal projection.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0279606-0
Keywords: Contraction operator, Fourier-Stieltjes coefficients, orthogonal projection
Article copyright: © Copyright 1971 American Mathematical Society