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arXiv · 2411.04911

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

Zenon Jan Jabłoński·Il Bong Jung·Jan Stochel
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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 $L^2(ρ)$-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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Zenon Jan Jabłoński, Il Bong Jung, Jan Stochel. 2024-11-07. When is a CPD weighted shift similar to a subnormal operator?. https://arxiv.org/abs/2411.04911

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