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

 

Another generalization of Anderson's theorem


Author: Hong Ke Du
Journal: Proc. Amer. Math. Soc. 123 (1995), 2709-2714
MSC: Primary 47B15; Secondary 47A30, 47A63, 47B47
MathSciNet review: 1273496
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Abstract: In this paper, we prove that if A and B are normal operators on a Hilbert space H, then, for every operator S satisfying $ ASB = S, \left\Vert {AXB - X + S} \right\Vert \geq {\left\Vert A \right\Vert^{ - 1}}{\left\Vert B \right\Vert^{ - 1}}\left\Vert S \right\Vert$ for all operators $ X \in B(H)$, and that if A and B are contractions, then, for every operator S satisfying $ ASB = S$ and $ {A^ \ast }S{B^ \ast } = S,\left\Vert {AXB - X + S} \right\Vert \geq \left\Vert S \right\Vert$ for all operators $ X \in B(H)$, where $ B(H)$ denotes the set of all bounded linear operators on H.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273496-1
PII: S 0002-9939(1995)1273496-1
Keywords: Derivation, contraction, normal operator, norm inequality
Article copyright: © Copyright 1995 American Mathematical Society