2012/02/17 by Haykel Gaaya, Gaaya, Haykel
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · doi:10.48550/arxiv.1202.3962
openalex publication_date 2012/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let denote by S(ϕ) the extremal operator defined by the compression of the unilateral shift S to the model subspace H(ϕ)=H2 \ominus ϕH2 as the following S(ϕ)f(z)=P(zf(z)), where P denotes the orthogonal projection from the Hardy space H2 onto H(ϕ) and ϕ is an inner function on the unit disc. In this mathematical notes, we give an explicit formula of the numerical radius of the truncated shift S(ϕ) in the particular case where ϕ is a finite Blaschke product with unique zero and an estimate on the general case. We establish also a sharpened Schwarz-Pick operatorial inequality generalizing a U. Haagerup and P. de la Harpe result for nilpotent operators