2013/03/26 by Piotr Budzyński, Zenon Jan Jabłoński, Budzynski, Piotr +5
Mathematics · #44A60 #47B20 #47B33 #47B37 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1303.6486
openalex publication_date 2013/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A criterion for subnormality of unbounded composition operators in L2-spaces, written in terms of measurable families of probability measures satisfying the so-called consistency condition, is established. It becomes a new characterization of subnormality in the case of bounded composition operators. Pseudo-moments of a measurable family of probability measures that satisfies the consistency condition are proved to be given by the Radon-Nikodym derivatives which appear in Lambert's characterization of bounded composition operators. A criterion for subnormality of composition operators induced by matrices is provided. The question of subnormality of composition operators over discrete measure spaces is studied. Two new classes of subnormal composition operators over discrete measure spaces are introduced. A recent criterion for subnormality of weighted shifts on directed trees by the present authors is essentially improved in the case of rootless directed trees and nonzero weights by dropping the assumption of density of C∞-vectors in the underlying L2-space.