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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-3,
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},
volume = {223},
year = {2014},
pages = {141-156},
zbl = {1298.47047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-3}
}
Yong Chen; Young Joo Lee; Tao Yu. Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space. Studia Mathematica, Tome 223 (2014) pp. 141-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-3/