2021/06/16 by Glenier Bello, Bello, Glenier, Dmitry V. Yakubovich +1
Mathematics · #47A20 #47A25 #47A63 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2106.08757
openalex publication_date 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an invertible linear operator T on a Hilbert space H, put α(T^*,T) := -T*2T2 + (1+r2) T^* T - r2 I, where I stands for the identity operator on H and r∈ (0,1); this expression comes from applying Agler's hereditary functional calculus to the polynomial α(t)=(1-t) (t-r2). We give a concrete unitarily equivalent functional model for operators satisfying α(T^*,T)≥0. In particular, we prove that the closed annulus r≤ |z|≤ 1 is a complete K-spectral set for T. We explain the relation of the model with the Sz.-Nagy--Foias one and with the observability gramian and discuss the relationship of this class with other operator classes related to the annulus.