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Inequalities for Trace Norms of 2 × 2 Block Matrices

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Abstract

This paper derives an inequality relating the p-norm of a positive 2×2 block matrix to the p-norm of the 2×2 matrix obtained by replacing each block by its p-norm. The inequality had been known for integer values of p, so the main contribution here is the extension to all values p≥1. In a special case the result reproduces Hanner’s inequality. A weaker inequality which applies also to non-positive matrices is presented. As an application in quantum information theory, the inequality is used to obtain some results concerning maximal p-norms of product channels.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Christopher King

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  1. Christopher King
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Correspondence to Christopher King.

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Communicated by M.B. Ruskai

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King, C. Inequalities for Trace Norms of 2 × 2 Block Matrices. Commun. Math. Phys. 242, 531–545 (2003). https://doi.org/10.1007/s00220-003-0955-9

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  • DOI: https://doi.org/10.1007/s00220-003-0955-9

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