Multiplication operators on the Bergman space via analytic continuation

Multiplication Operators on the Bergman Space via Analytic Continuation

ABSTRACT. In this paper, using the group-like property of local inverses of a finite Blaschke product φ, we will show that the largest C-algebra in the commutant of the multiplication operator Mφ by φ on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of φ ◦ φ over the unit disk. If the order of the Blaschke product φ i...

Positive Toeplitz Operators on the Bergman Space

In this paper we find conditions on the existence of bounded linear operators A on the Bergman space La(D) such that ATφA ≥ Sψ and ATφA ≥ Tφ where Tφ is a positive Toeplitz operator on L 2 a(D) and Sψ is a self-adjoint little Hankel operator on La(D) with symbols φ, ψ ∈ L∞(D) respectively. Also we show that if Tφ is a non-negative Toeplitz operator then there exists a rank one operator R1 on L ...

Intermediate Hankel Operators on the Bergman Space

Analytic Continuation in Bergman Spaces and the Compression of Certain Toeplitz Operators

Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A2(G\K) and A2 (G) be the Bergman spaces on G\K, respectively G and define N = A2(G\K) e A2 (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of 8G that do not intersect K. This result will be used to discuss the Fredholm theory of t...

Self-commutators of composition operators with monomial symbols on the Bergman space

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...