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Proceedings of the American Mathematical Society

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

 

 

A property of weakly compact operators on $ C[0,1]$


Author: James R. Holub
Journal: Proc. Amer. Math. Soc. 97 (1986), 396-398
MSC: Primary 47B05; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1986-0840617-6
MathSciNet review: 840617
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Abstract: It is shown that if $ T$ is a bounded linear operator on $ C[0,1]$ then either $ \vert\vert I + T\vert\vert$ or $ \vert\vert I - T\vert\vert$ equals $ 1 + \vert\vert T\vert\vert$. If $ T$ is a weakly compact operator then $ \vert\vert I + T\vert\vert = 1 + \vert\vert T\vert\vert$, an extension of a result of Daugavet concerning compact operators on $ C[0,1]$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840617-6
Keywords: Weakly compact operator on $ C[0,1]$, Daugavet's equation, operator norm equalities
Article copyright: © Copyright 1986 American Mathematical Society