arXiv 2106.090922021-06math.FA

Norm inequalities for the spectral spread of Hermitian operators

Pedro Massey, Demetrio Stojanoff, Sebastian Zarate

备注：: 26 pages. Revised version with several changes

英文摘要：

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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