2021/06/16 by Pedro Massey, Massey, Pedro, Demetrio Stojanoff +3
Mathematics · Physics and Astronomy · #47A30 #47B10 #47B15 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2106.09092
openalex publication_date 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).