Geodesic
Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
Yong Chen1 ; Young Joo Lee2 ; Tao Yu1
1Department of Mathematics Zhejiang Normal University Jinhua, 321004, P.R. China
2Department of Mathematics Chonnam National University Gwangju 500-757, Korea
Studia Mathematica, Tome 220 (2014) no. 2, pp. 141-156
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 $.
DOI : 10.4064/sm220-2-3
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

Yong Chen  1   ; Young Joo Lee  2   ; Tao Yu  1

1 Department of Mathematics Zhejiang Normal University Jinhua, 321004, P.R. China
2 Department of Mathematics Chonnam National University Gwangju 500-757, Korea 
@article{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},
     pages = {141--156},
     year = {2014},
     volume = {220},
     number = {2},
     doi = {10.4064/sm220-2-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm220-2-3/}
}
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
SP  - 141
EP  - 156
VL  - 220
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm220-2-3/
DO  - 10.4064/sm220-2-3
LA  - en
ID  - 10_4064_sm220_2_3
ER  - 
%0 Journal Article
%A Yong Chen
%A Young Joo Lee
%A Tao Yu
%T Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
%J Studia Mathematica
%D 2014
%P 141-156
%V 220
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm220-2-3/
%R 10.4064/sm220-2-3
%G en
%F 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 220 (2014) no. 2, pp. 141-156. doi: 10.4064/sm220-2-3

Cité par Sources :