Schatten p-norm inequalities related to a characterization of inner product spaces

Details Schatten p-norm inequalities related to a characterization of inner product spaces Schatten p-norm inequalities related to a characterization of inner product spaces

2008-01-17

arxiv.org/abs/0801.2726v2

Math. Inequal. Appl. 13 (2010), no. 2, 235-241

Mathematics

Functional Analysis

Minor revision, to appear in Math. Inequal. Appl. (MIA)

Scientific paper

Let $A_1, ... A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, ... A_n$ belong to a Schatten $p$-class, for some $p>0$, then 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq \sum_{i,j=1}^n\|A_i\pm A_j\|^p_p for $0

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