Norm inequalities for the spectral spread of Hermitian operators

P. MASSEY , D. STOJANOFF Y S, 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 ofa Hermitian (self-adjoint) operator acting on a separable innite dimensional Hilbertspace that we call spectral spread. Then, we obtain some submajorization inequalitiesinvolving the spectral spread of self-adjoint operators, that are related to Tao´s inequal-ities for anti-diagonal blocks of positive operators, Kittaneh´s commutator inequalitiesfor 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).