Toeplitz and Hankel operators on Bergman one 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

Toeplitz algebra and Hankel algebra on the harmonic Bergman space

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.  2002 Elsevier Science (USA). All rights reserved.

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...