Commutator inequalities associated with the polar decomposition

Author:
Fuad Kittaneh

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1279-1283

MSC (2000):
Primary 15A23, 15A57, 15A60, 47A30, 47B47

DOI:
https://doi.org/10.1090/S0002-9939-01-06197-4

Published electronically:
October 12, 2001

MathSciNet review:
1879948

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a polar decomposition of an complex matrix . Then for every unitarily invariant norm , it is shown that

where denotes the operator norm. This is a quantitative version of the well-known result that is normal if and only if . Related inequalities involving self-commutators are also obtained.

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Additional Information

**Fuad Kittaneh**

Affiliation:
Department of Mathematics, University of Jordan, Amman, Jordan

Email:
fkitt@ju.edu.jo

DOI:
https://doi.org/10.1090/S0002-9939-01-06197-4

Keywords:
Commutator,
polar decomposition,
positive semidefinite matrix,
unitarily invariant norm

Received by editor(s):
December 14, 1999

Received by editor(s) in revised form:
November 1, 2000

Published electronically:
October 12, 2001

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society