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arXiv · 2106.09092

Norm inequalities for the spectral spread of Hermitian operators

Pedro Massey·Demetrio Stojanoff·Sebastian Zarate
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Abstract

In this work we introduce a new measure for the dispersion of the spectral scale of a Hermitian (self-adjoint) operator acting on a separable infinite dimensional Hilbert space that we call spectral spread. Then, we obtain some submajorization inequalities involving the spectral spread of self-adjoint operators, that are related to Tao's inequalities for anti-diagonal blocks of positive operators, Kittaneh's commutator inequalities for positive operators and also related to the Arithmetic-Geometric mean inequality. In turn, these submajorization relations imply inequalities for unitarily invariant norms (in the compact case).

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Pedro Massey, Demetrio Stojanoff, Sebastian Zarate. 2021-06-16. Norm inequalities for the spectral spread of Hermitian operators. https://arxiv.org/abs/2106.09092

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