Norm inequalities for operators with positive real part

Bhatia, Rajendra ; Zhan, Xingzhi (2003) Norm inequalities for operators with positive real part Journal of Operator Theory, 50 . pp. 67-76. ISSN 0379-4024

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Let T = A + iB with A positive semidefinite and B Hermitian. We derive a majorisation relation involving the singular values of T,A, and B. As a corollary, we show that ||T||2p≤||A||2p+21−2/p||B||2p, for all p≥2; and that this inequality is sharp. When 1≤p≤2 this inequality is reversed. For p = 1, we prove the sharper inequality ||T||21 ≥ ||A||21+||B||21. Such inequalities are useful in studying the geometry of Schatten spaces, and our results include and improve upon earlier results proved in this context. Some related inequalities are also proved in the paper.

Item Type:Article
Source:Copyright of this article belongs to Theta Foundation.
Keywords:Positive Operators; Singular Values; Majorisation; Schatten Pnorms; Inequalities
ID Code:97486
Deposited On:20 Feb 2013 09:04
Last Modified:20 Feb 2013 09:07

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