Norm attaining operators and simultaneously continuous retractions
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- by Jerry Johnson and John Wolfe PDF
- Proc. Amer. Math. Soc. 86 (1982), 609-612 Request permission
Abstract:
A compact metric space $S$ is constructed and it is shown that there is a bounded linear operator $T:{L^1}[0,1] \to C(S)$ which cannot be approximated by a norm attaining operator. Also it is established that there does not exist a retract of ${L^\infty }[0,1]$ onto its unit ball which is simultaneously weak* continuous and norm uniformly continuous.References
- Y. Benyamini, Small into-isomorphisms between spaces of continuous functions, Proc. Amer. Math. Soc. 83 (1981), no. 3, 479–485. MR 627674, DOI 10.1090/S0002-9939-1981-0627674-2 —, Simultaneously continuous retractions on the unit wall of a Banach space, preprint. N. Dunford and J. T. Schwartz, Linear operators, Part I, Interscience, New York, 1958.
- Jerry Johnson and John Wolfe, Norm attaining operators, Studia Math. 65 (1979), no. 1, 7–19. MR 554537, DOI 10.4064/sm-65-1-7-19
- Walter Schachermayer, Norm attaining operators on some classical Banach spaces, Pacific J. Math. 105 (1983), no. 2, 427–438. MR 691613
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 609-612
- MSC: Primary 47B38; Secondary 46B25
- DOI: https://doi.org/10.1090/S0002-9939-1982-0674091-6
- MathSciNet review: 674091