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

Yong Chen, Young Joo Lee, and Tao Yu. "Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space." Studia Mathematica 220.2 (2014): 141-156. <http://eudml.org/doc/285564>.

@article{YongChen2014,
abstract = {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 ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if ϕ = λz² for some unimodular constant λ.},
author = {Yong Chen, Young Joo Lee, Tao Yu},
journal = {Studia Mathematica},
keywords = {Dirichlet space; multiplication operator; reducing subspace},
language = {eng},
number = {2},
pages = {141-156},
title = {Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space},
url = {http://eudml.org/doc/285564},
volume = {220},
year = {2014},
}

TY - JOUR
AU - Yong Chen
AU - Young Joo Lee
AU - Tao Yu
TI - Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
JO - Studia Mathematica
PY - 2014
VL - 220
IS - 2
SP - 141
EP - 156
AB - 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 ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if ϕ = λz² for some unimodular constant λ.
LA - eng
KW - Dirichlet space; multiplication operator; reducing subspace
UR - http://eudml.org/doc/285564
ER -