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).
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