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Proceedings of the American Mathematical Society

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Isometries on $ L\sp{p}$ spaces and copies of $ l\sp{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?)

  • [1] S. L. Campbell, G. D. Faulkner and Robert Sine, Isometries, projections, and Wold decompositions (to appear). MR 579023 (81k:47041)
  • [2] J. Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 2 (1958), 459-466. MR 0105017 (21:3764)

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

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