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Journal of the London Mathematical Society 1988 s2-37(121):148-157; doi:10.1112/jlms/s2-37.121.148
© 1988 by London Mathematical Society
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© The London Mathematical Society

Lipschitz Continuity of Functions of Operators in the Schatten Classes

E. B. Davies

Department of Mathematics, King's College Strand, London WC2R 2LS

Received 3 November 1986.

We show that the operator-valued map A -> f(A) is Lipschitz continuous with respect to the Schatten p-norm if 1 < p < {infty} and


Formula

where µ is a signed measure of R of compact support. In the particular case in which f(u) = |u| this result is false for p = 1 and p = {infty}, but results only marginally (logarithmically) weaker do hold in finite dimensions.


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