Hankel operators and Toeplitz operators on the Bergman space

Toeplitz and Hankel Operators on a Vector-valued Bergman Space

In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces L2,C n a (D), where D is the open unit disk in C and n ≥ 1. We show that the set of all Toeplitz operators TΦ,Φ ∈ LMn(D) is strongly dense in the set of all bounded linear operators L(L2,Cn a (D)) and characterize all finite rank little Hankel operators.

Intermediate Hankel Operators on the Bergman Space

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 ...

Toeplitz and Hankel Operators with Radial Symbol on the Bergman Space

Let dA denote Lebesgue area measure on the unit disk D, normalized so that the measure of D equals 1. For α > −1, we denote by dAα the measure dAα(z) = (α + 1)(1 − |z|2)αdA(z). For 1 ≤ p < +∞, the space L(D, dAα) is a Banach space. The weighted Bergman space Aα is the closed subspace of analytic functions in the Hilbert space L(D, dAα). For each z ∈ D, the application:Lz : A 2 α −→ C is continu...

Spectral theory of Toeplitz and Hankel operators on the Bergman space A^1

The Fredholm properties of Toeplitz operators on the Bergman space A have been well-known for continuous symbols since the 1970s. We investigate the case p = 1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on A that ari...