A generalization of a theorem of J. Holub-Reference-Cited by-同舟云学术

A generalization of a theorem of J. Holub

Published:1990 Issue:4 Volume:108 Page:937-939
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Abramovich Yuri

Abstract

We present here a simple proof of the following result: Let X X be an arbitrary C ( K ) C(K) or L 1 ( μ ) {L_1}(\mu ) space and let T : X → X T:X \to X be an arbitrary linear continuous operator. Then for at least one choice of signs. \[ ‖ I ± T ‖ = 1 + ‖ T ‖ . \left \| {I \pm T} \right \| = 1 + \left \| T \right \|. \] This is a slightly generalized version of a recent result due to J. Holub [4].

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1990-108-04/S0002-9939-1990-1002149-5/S0002-9939-1990-1002149-5.pdf

Reference6 articles.

1. Y. A. Abramovich, Injective envelopes of normed lattices, Soviet Math. Dokl. 12 (1971), 511-514.

2. Y. A. Abramovich and K. Schmidt, Daugavet’s equation and orthomorphisms, preprint.

3. Pure and Applied Mathematics;Aliprantis, Charalambos D.,1985

4. A property of weakly compact operators on 𝐶[0,1];Holub, James R.;Proc. Amer. Math. Soc.,1986

5. Daugavet’s equation and operators on 𝐿¹(𝜇);Holub, James R.;Proc. Amer. Math. Soc.,1987

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