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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of a theorem of J. Holub


Author: Yuri Abramovich
Journal: Proc. Amer. Math. Soc. 108 (1990), 937-939
MSC: Primary 47B38; Secondary 47A30
MathSciNet review: 1002149
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Abstract: We present here a simple proof of the following result: Let $ X$ be an arbitrary $ C(K)$ or $ {L_1}(\mu )$ space and let $ T:X \to X$ be an arbitrary linear continuous operator. Then for at least one choice of signs.

$\displaystyle \left\Vert {I \pm T} \right\Vert = 1 + \left\Vert T \right\Vert.$

This is a slightly generalized version of a recent result due to J. Holub [4].

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1002149-5
PII: S 0002-9939(1990)1002149-5
Article copyright: © Copyright 1990 American Mathematical Society