2015/12/15 by Erik Christensen, Christensen, Erik
Mathematics · Physics and Astronomy · #46L55 #47D06 #58B34 #81S05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #math.OA #msc:46L55 #msc:47D06 #msc:58B34 #msc:81S05
paper · pdf · doi:10.48550/arxiv.1512.04979
16 pages
arxiv created 2015/12/15 · openalex publication_date 2015/12/15 · arxiv updated 2015/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some complex Borel functions g(t) we establish inequalities of the type ||[g(D),y]|| ≤ A|||y|| + B||[D,y]|| + ...+ X|[D, [D,...[D, y]...]]||. The proofs take place in a space of infinite matrices with operator entries, and in this setting it is possible to approximate the matrix associated to [g(D), y] by the Schur product of a matrix approximating [D,y] and a scalar matrix. A classical inequality of Bennett on the norm of Schur products may then be applied to obtain the results.