Distance between Hermitian operators in Schatten classes

Bhatia, Rajendra ; Šemrl, Peter (1996) Distance between Hermitian operators in Schatten classes Proceedings of the Edinburgh Mathematical Society, 39 (2). pp. 377-380. ISSN 0013-0915

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Official URL: http://journals.cambridge.org/abstract_S0013091500...

Related URL: http://dx.doi.org/10.1017/S0013091500023105


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 is < p is < ∞, 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.

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