A property of weakly compact operators on $C[0,1]$
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- by James R. Holub PDF
- Proc. Amer. Math. Soc. 97 (1986), 396-398 Request permission
Abstract:
It is shown that if $T$ is a bounded linear operator on $C[0,1]$ then either $||I + T||$ or $||I - T||$ equals $1 + ||T||$. If $T$ is a weakly compact operator then $||I + T|| = 1 + ||T||$, an extension of a result of Daugavet concerning compact operators on $C[0,1]$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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