Compact operators on the weighted Bergman space A¹(ψ)

• Autorzy: Tao Yu
• Języki publikacji: EN

Abstrakty

EN

We show that a bounded linear operator S on the weighted Bergman space A¹(ψ) is compact and the predual space A₀(φ) of A¹(ψ) is invariant under S* if and only if $Sk_{z} → 0$ as z → ∂D, where $k_{z}$ is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.

Kategorie tematyczne

• 47A15: Invariant subspaces
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 177
• Numer: 3
• Strony: 277-284

Daty

wydano

2006

Twórcy

autor

Tao Yu

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

Identyfikatory

DOI

10.4064/sm177-3-6