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Bulletin of the London Mathematical Society Advance Access published online on September 23, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp078
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© 2009 London Mathematical Society

Non-commutative Hardy inequalities

Frank Hansen

Department of Economics
University of Copenhagen
Studiestraede 6
DK-1455 Copenhagen K
Denmark

Received 8 January 2009. Revision received 27 May 2009.

We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1 < p ≤ 2, and to operators under a trace for arbitrary p > 1. Applications to trace functions are given. We introduce the tracial geometric mean and generalize Carleman's inequality.

2000 Mathematics Subject Classification 47A63, 26D15.


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