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Proceedings of the American Mathematical Society

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Isometries on $L^{p}$ spaces and copies of $l^{p}$ shifts

Authors: Stephen L. Campbell, Gary D. Faulkner and Marianne L. Gardner
Journal: Proc. Amer. Math. Soc. 77 (1979), 198-200
MSC: Primary 47A15; Secondary 47B37
MathSciNet review: 542084
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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 [Enhancements On Off] (What's this?)

  • 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

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Keywords: Isometries, invariant subspaces, shifts in Banach spaces
Article copyright: © Copyright 1979 American Mathematical Society