Commutator inequalities associated with the polar decomposition
نویسندگان
چکیده
منابع مشابه
Commutator Inequalities Associated with the Polar Decomposition
Let A = UP be a polar decomposition of an n×n complex matrix A. Then for every unitarily invariant norm ||| · |||, it is shown that ||| |UP − PU |||| ≤ |||A∗A−AA∗||| ≤ ‖UP + PU‖ |||UP − PU |||, where ‖·‖ denotes the operator norm. This is a quantitative version of the wellknown result that A is normal if and only if UP = PU . Related inequalities involving self-commutators are also obtained.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-06197-4