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Proceedings of the American Mathematical Society

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

 

 

Norm attaining operators and simultaneously continuous retractions


Authors: Jerry Johnson and John Wolfe
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0674091-6
Article copyright: © Copyright 1982 American Mathematical Society