On a Class of Composition Operators on Bergman Space

On a Class of Composition Operators on Bergman Space

Let D= {z ∈ C : |z| < 1} be the open unit disk in the complex plane C. Let A2(D) be the space of analytic functions on D square integrable with respect to the measure dA(z) = (1/π)dx dy. Given a ∈D and f any measurable function on D, we define the function Ca f by Ca f (z) = f (φa(z)), where φa ∈ Aut(D). The map Ca is a composition operator on L2(D,dA) and A2(D) for all a ∈D. Let (A2(D)) be the...

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_...

Schatten Class Toeplitz Operators on the Bergman Space

Namita Das P. G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, Orissa 751004, India Correspondence should be addressed to Namita Das, [email protected] Received 23 July 2009; Revised 7 September 2009; Accepted 14 October 2009 Recommended by Palle Jorgensen We have shown that if the Toeplitz operator Tφ on the Bergman space La D belongs to the Schatten class Sp, 1 ≤...

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