Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-02T21:34:41.053Z Has data issue: false hasContentIssue false
  • English
  • Français

Distance between Hermitian operators in Schatten classes

Published online by Cambridge University Press:  20 January 2009

Rajendra Bhatia  and
Peter Šemrl
Rajendra Bhatia
Affiliation:
Indian Statistical Institute New Delhi-110016, India
Peter Šemrl
Affiliation:
University of Maribor Smetanova 17 P.O. Box 224 62000 Maribor Slovenia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the distance between a fixed Hermitian operator B and the unitary orbit of another Hermitian operator A and show that in each Schatten p-class, 1<p<∞, critical points of this distance function are at operators commuting with B. As a consequence we obtain a perturbation bound for the eigenvalues of Hermitian operators in these Schatten classes.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 377 - 380
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Aiken, J. G., Erdos, J. A. and Goldstein, J. A., Unitary approximation of positive operators, Illinois J. Math. 24 (1980), 61–72.CrossRefGoogle Scholar
2. Bhatia, R., Perturbation bounds for matrix eigenvalues (Pitman Res. Notes Math. 162 (Longman, Harlow, 1987).Google Scholar
3. Bhatia, R. and Elsner, L., The Hoffman-Wielandt inequality in infinite dimensions, Proc. Indian Acad. Sci. Math. Sci., to appear.Google Scholar
4. Cochran, J. A. and Hinds, E. W., Improved error bounds for the eigenvalues of certain normal operators, SIAM J. Numer. Anal. 9 (1972), 446–453.CrossRefGoogle Scholar
5. Friedland, S., Inverse eigenvalue problems, Linear Algebra Appl. 17 (1977), 15–51.CrossRefGoogle Scholar
6. Markus, A. S., The eigen and singular values of the sum and product of linear operators, Russian Math. Surveys 19 (1964), 92–120.CrossRefGoogle Scholar