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Journal of the London Mathematical Society 1989 s2-39(2):299-308; doi:10.1112/jlms/s2-39.2.299
© 1989 by London Mathematical Society
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© Oxford University Press

Some Commutator Estimates in the Schatten Classes

A. Abdessemed and E. B. Davies

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

We prove inequalities of the type |||A|B–B|A|||p ≤ kp||AB – BA||p for various classes of bounded operators on a Hilbert space, and various values of p in the range 1 < p < {infty}, where || ||p denotes the Schatten p-norm.

Permanent address of first author. 45 Kitouni Abdelmalek, Constantine, Algeria


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