When is a CPD weighted shift similar to a subnormal operator?

2024/11/07 by Zenon Jan Jabłoński, Il Bong Jung, Jabłoński, Zenon Jan +3
Mathematics · #Advanced Topics in Algebra #Advanced Banach Space Theory #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2411.04911

Abstract

We prove that a CPD unilateral weighted shift W_λ of type III is a quasi-affine transform of the operator M_z of multiplication by the independent variable on the L²(ρ)-closure of analytic complex polynomials on the complex plane, where ρ is a measure precisely determined by W_λ. By using this model, we provide necessary and sufficient conditions for similarity of W_λ to M_z. Necessary conditions for a CPD operator to be similar to a subnormal one are given. A variety of concrete classes of non-subnormal CPD unilateral weighted shifts similar to subnormal operators are established.

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