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Article Dans Une Revue Linear Algebra and its Applications Année : 2020

Clarkson-McCarthy inequalities with unitary and isometry orbits

Résumé

A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten p-classes for p > 2 is proved: if A, B are two n-by-n matrices, then there exists some pair of n-by-n unitary matrices U, V such that U A + B 2 p U * + V A − B 2 p V * ≤ |A| p + |B| p 2. A similar statement holds for compact Hilbert space operators. Another improvement of McCarthy's inequality is given via the new operator parallelogramm law, |A + B| 2 ⊕ |A − B| 2 = U 0 (|A| 2 + |B| 2)U * 0 + V 0 (|A| 2 + |B| 2)V * 0 for some pair of 2n-by-n isometry matrices U 0 , V 0 .
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hal-03526785 , version 1 (14-01-2022)

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  • HAL Id : hal-03526785 , version 1

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Jean-Christophe Bourin, Eun-Young Lee. Clarkson-McCarthy inequalities with unitary and isometry orbits. Linear Algebra and its Applications, 2020. ⟨hal-03526785⟩
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