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Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space

Tom 220 / 2014

Yong Chen, Young Joo Lee, Tao Yu Studia Mathematica 220 (2014), 141-156 MSC: Primary 47B35; Secondary 32A36. DOI: 10.4064/sm220-2-3

Streszczenie

We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier $\phi $ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if $\phi =\lambda z^2$ for some unimodular constant $\lambda $.

Autorzy

  • Yong ChenDepartment of Mathematics
    Zhejiang Normal University
    Jinhua, 321004, P.R. China
    e-mail
  • Young Joo LeeDepartment of Mathematics
    Chonnam National University
    Gwangju 500-757, Korea
    e-mail
  • Tao YuDepartment of Mathematics
    Zhejiang Normal University
    Jinhua, 321004, P.R. China
    e-mail

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