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New operator inequalities in finite-dimensional vector spaces

Author: Alexander Y. Gordon
Journal: Proc. Amer. Math. Soc. 143 (2015), 4613-4622
MSC (2010): Primary 15A45, 47A63; Secondary 39A70
Published electronically: July 1, 2015
MathSciNet review: 3391021
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish some new operator inequalities in an $ n$-dimensional vector space $ X$ equipped with a seminorm $ \Vert\cdot \Vert$. Here is an example. If $ A$ is an invertible linear operator in $ X$ and $ \xi $ is a vector, then

$\displaystyle \Vert\xi \Vert^r \le \sum _{1\le \vert j\vert\le {n+r-1\choose r}}\Vert A^j\xi \Vert^r.$

Some special cases have been known and used in mathematical physics.

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

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Additional Information

Alexander Y. Gordon
Affiliation: Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, North Carolina 28223

Received by editor(s): July 21, 2014
Published electronically: July 1, 2015
Communicated by: Michael Hitrik
Article copyright: © Copyright 2015 American Mathematical Society

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