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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Isometries on $L^{p}$ spaces and copies of $l^{p}$ shifts
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by Stephen L. Campbell, Gary D. Faulkner and Marianne L. Gardner PDF
Proc. Amer. Math. Soc. 77 (1979), 198-200 Request permission

Abstract:

Necessary and sufficient conditions are given on an isometry V in an ${L^p}$ space so that there exists an invariant subspace M such that V restricted to M is isometrically equivalent to the unilateral shift on ${l^p}$.
References
  • S. Campbell, G. Faulkner, and R. Sine, Isometries, projections and Wold decompositions, Operator theory and functional analysis (Papers, Summer Meeting, Amer. Math. Soc., Providence, R.I., 1978) Res. Notes in Math., vol. 38, Pitman, Boston, Mass.-London, 1979, pp. 85–114. MR 579023
  • John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459–466. MR 105017, DOI 10.2140/pjm.1958.8.459
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 77 (1979), 198-200
  • MSC: Primary 47A15; Secondary 47B37
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0542084-5
  • MathSciNet review: 542084