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Mathematics  2008 

Non-commutative Hardy inequalities

DOI: 10.1112/blms/bdp078

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Abstract:

We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 11. Applications to trace functions are given. We introduce the tracial geometric mean and generalize Carleman's inequality. Key words and phrases: Hardy's inequality, positive operator, trace function, geometric mean, Carleman's inequality.

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