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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Characterization of the flip operator
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by H. A. Seid
Proc. Amer. Math. Soc. 46 (1974), 253-258
DOI: https://doi.org/10.1090/S0002-9939-1974-0350493-8
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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
  • Paul R. Halmos, Measure Theory, D. Van Nostrand Co., 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 Company, 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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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 46 (1974), 253-258
  • MSC: Primary 47B37
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0350493-8
  • MathSciNet review: 0350493