2001
DOI: 10.1090/s0002-9939-01-06197-4
|View full text |Cite
|
Sign up to set email alerts
|

Commutator inequalities associated with the polar decomposition

Abstract: Abstract. Let A = UP be a polar decomposition of an n × n complex matrix A. Then for every unitarily invariant norm ||| · |||, it is shown thatwhere · denotes the operator norm. This is a quantitative version of the wellknown result that A is normal if and only if UP = P U. Related inequalities involving self-commutators are also obtained.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
1
0

Year Published

2007
2007
2023
2023

Publication Types

Select...
5
1

Relationship

1
5

Authors

Journals

citations
Cited by 16 publications
(1 citation statement)
references
References 10 publications
0
1
0
Order By: Relevance
“…1]. To claim the same for the right hand inequality we first note that 2 T 2 ≤ T * T + T T * (see [7]). From the right hand inequality obtained in Theorem 2.11 we get,…”
Section: Resultsmentioning
confidence: 86%
“…1]. To claim the same for the right hand inequality we first note that 2 T 2 ≤ T * T + T T * (see [7]). From the right hand inequality obtained in Theorem 2.11 we get,…”
Section: Resultsmentioning
confidence: 86%