Norm inequalities for the spectral spread of Hermitian operators

PEDRO MASSEY; DEMETRIO STOJANOFF; SEBASTIAN ZÁRATE

MATHEMATISCHE NACHRICHTEN

WILEY-V C H VERLAG GMBH

Lugar: Weinheim; Año: 2023

0025-584X

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).