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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
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Abstract

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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

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