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Compact operators on the weighted Bergman space A¹(ψ)

100%

Yu T.

Studia Mathematica

2006

tom 177

nr 3

277-284

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.

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

51%

Chen Y., Lee Y., Yu T.

Studia Mathematica

2014

tom 220

nr 2

141-156

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.

Ograniczanie wyników

2 Studia Mathematica

2 Yu T.

1 Chen Y.

1 Lee Y.

1 2014

1 2006

Wyniki wyszukiwania

Compact operators on the weighted Bergman space A¹(ψ)

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