Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
Studia Mathematica, Tome 220 (2014) no. 2, pp. 141-156
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $.
Keywords:
consider reducibility unitary equivalence multiplication operators dirichlet space first characterize reducibility multiplication operator induced finite blaschke product application multiplication operator induced blaschke product zeros reducible only obvious prove multiplication operator induced multiplier phi unitarily equivalent weighted shift multiplicity only phi lambda unimodular constant lambda
Affiliations des auteurs :
Yong Chen 1 ; Young Joo Lee 2 ; Tao Yu 1
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author = {Yong Chen and Young Joo Lee and Tao Yu},
title = {Reducibility and unitary equivalence for a class of multiplication operators on the {Dirichlet} space},
journal = {Studia Mathematica},
pages = {141--156},
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volume = {220},
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year = {2014},
doi = {10.4064/sm220-2-3},
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Yong Chen; Young Joo Lee; Tao Yu. Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space. Studia Mathematica, Tome 220 (2014) no. 2, pp. 141-156. doi: 10.4064/sm220-2-3
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