2017/10/20 by Sibaprasad Barik, Barik, Sibaprasad, B. Krishna Das +5 · 1 citation
Mathematics · #32A35 #32A70 #46E22 #47A13 #47A20 #47A45 #47A56 #47B32 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1710.07624
openalex publication_date 2017/10/20 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The celebrated Sz.-Nagy and Foias and Ando theorems state that a single\ncontraction, or a pair of commuting contractions, acting on a Hilbert space\nalways possesses isometric dilation and subsequently satisfies the von Neumann\ninequality for polynomials in \ℂ[z] or \ℂ[z1, z2],\nrespectively. However, in general, neither the existence of isometric dilation\nnor the von Neumann inequality holds for n-tuples, n \≥ 3, of commuting\ncontractions. The goal of this paper is to provide a taste of the isometric\ndilations, the von Neumann inequality and a sharper version of von Neumann\ninequality for a large class of n-tuples, n \≥ 3, of commuting\ncontractions.\n