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The Iterates of a Contraction and its Adjoint
John A. R. Holbrook
Proceedings of the American Mathematical Society
Vol. 29, No. 3 (Aug., 1971), pp. 543-546
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2038594
Page Count: 4
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We prove that when $T$ is a contraction on Hilbert space the size of $\lim \sup|((T^\ast)^nh, g)|$ is controlled by that of $\lim \sup|(T^nh, g)|$. We give an application to Fourier-Stieltjes coefficients. Important in the proof is a generalization of the technique of orthogonal projection.
Proceedings of the American Mathematical Society © 1971 American Mathematical Society