The iterates of a contraction and its adjoint
HTML articles powered by AMS MathViewer
- by John A. R. Holbrook PDF
- Proc. Amer. Math. Soc. 29 (1971), 543-546 Request permission
Abstract:
We prove that when T is a contraction on Hilbert space the size of $|({({T^\ast })^n}h,g)|$ is controlled by that of $\lim \sup |({T^n}h,g)|$. We give an application to Fourier-Stieltjes coefficients. Important in the proof is a generalization of the technique of orthogonal projection.References
- Shaul R. Foguel, Powers of a contraction in Hilbert space, Pacific J. Math. 13 (1963), 551–562. MR 163170
- S. R. Foguel, A counterexample to a problem of Sz.-Nagy, Proc. Amer. Math. Soc. 15 (1964), 788–790. MR 165362, DOI 10.1090/S0002-9939-1964-0165362-X B. Sz.-Nagy and C. Foiaş, Analyse harmonique des opérateurs de l’espace de Hilbert, Masson, Paris; Akad. Kiadó, Budapest, 1967. MR 37 #778.
- P. R. Halmos, On Foguel’s answer to Nagy’s question, Proc. Amer. Math. Soc. 15 (1964), 791–793. MR 165363, DOI 10.1090/S0002-9939-1964-0165363-1
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
- K. de Leeuw and Y. Katznelson, The two sides of a Fourier-Stieltjes transform and almost idempotent measures, Israel J. Math. 8 (1970), 213–229. MR 275060, DOI 10.1007/BF02771559
Additional Information
- © Copyright 1971 American Mathematical Society
- 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