Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A note on "More Operator Versions of the Schwarz Inequality"

A note on "More Operator Versions of the Schwarz Inequality" It is shown that for any (n + 1)-positive (possibly non-linear) map Φ and any bounded linear operators A i ,i = 1,¨,n we have [Φ(A i * A j )] i,j = 1 *≥[Φ(A i )*Φ(A j )] i,j = 1 *, and that the statement is false if "(n + 1)-positive" is replaced by "n-positive". This resolves an issue raised by Bhatia and Davis in relation to a Schwartz inequality which can be regarded as a non-commutative variance-covariance inequality [2] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A note on "More Operator Versions of the Schwarz Inequality"

Mathias, Roy
Positivity , Volume 8 (1) – Oct 21, 2004
Download PDF
3 pages

Loading next page...
 
/lp/springer_journal/a-note-on-more-operator-versions-of-the-schwarz-inequality-J0YnfJ20lB

References (7)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1023/B:POST.0000023200.14261.fc
Publisher site
See Article on Publisher Site

Abstract

It is shown that for any (n + 1)-positive (possibly non-linear) map Φ and any bounded linear operators A i ,i = 1,¨,n we have [Φ(A i * A j )] i,j = 1 *≥[Φ(A i )*Φ(A j )] i,j = 1 *, and that the statement is false if "(n + 1)-positive" is replaced by "n-positive". This resolves an issue raised by Bhatia and Davis in relation to a Schwartz inequality which can be regarded as a non-commutative variance-covariance inequality [2]

Journal

Positivity – Springer Journals

Published: Oct 21, 2004

There are no references for this article.