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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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].

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B38, 47A30

Retrieve articles in all journals with MSC: 47B38, 47A30

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society