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Proceedings of the American Mathematical Society

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Characterization of the flip operator

Author: H. A. Seid
Journal: Proc. Amer. Math. Soc. 46 (1974), 253-258
MSC: Primary 47B37
MathSciNet review: 0350493
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Abstract: The flip operator $F$ on ${L_p}([0,1])$, defined by $F(f)(t) = f(1 - t)$, for $f$ in ${L_p}([0,1])$ is characterized up to isometric transformation by means of its induced $\sigma$-isomorphism on the Borel sets of $[0,1]$.

References [Enhancements On Off] (What's this?)

  • Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
  • John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459–466. MR 105017
  • H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
  • H. A. Seid, Cyclic multiplication operators on ${L_p}$-spaces, Pacific J. Math. (to appear).

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Article copyright: © Copyright 1974 American Mathematical Society