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

• Autorzy: Yong Chen , Young Joo Lee , Tao Yu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32A36: Bergman spaces
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 220
• Numer: 2
• Strony: 141-156

Daty

wydano

2014

Twórcy

autor

Yong Chen

• Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P.R. China

autor

Young Joo Lee

• Department of Mathematics, Chonnam National University, Gwangju 500-757, Korea

autor

Tao Yu

• Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P.R. China

Identyfikatory

DOI

10.4064/sm220-2-3