2002/03/01 by Catalin Badea, Cătălin Badea, Gilles Cassier · 3 citations
Mathematics · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.FA #msc:47A30 #msc:47A63
paper · pdf · doi:10.1006/aima.2001.2035
published as Advances in Math. 166(2002), 260-297 · Preprint version
openalex publication_date 2002/03/01 · arxiv created 2005/01/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An equivalent formulation of the von Neumann inequality states that the backward shift S^* on ℓ2 is extremal, in the sense that if T is a Hilbert space contraction, then ‖p(T)‖ ≤ ‖p(S^*)‖ for each polynomial p. We discuss several results of the following type : if T is a Hilbert space contraction satisfying some constraints, then S^* restricted to a suitable invariant subspace is an extremal operator. Several operator radii are used instead of the operator norm. Applications to inequalities of coefficients of rational functions positive on the torus are given.