Toeplitz and Hankel Operators on a Vector-valued Bergman Space

Document Type : Original Article

Author

Namita Das

Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, 751004,, Odisha, India

10.22034/kjm.2015.13167

Abstract

In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces $L_a^{2, \mathbb{C}^n}(\mathbb{D})$, where $\mathbb{D}$ is the open unit disk in $\mathbb{C}$ and $n\geq 1.$ We show that the set of all Toeplitz operators $T_{\Phi}, \Phi\in L_{M_n}^{\infty}(\mathbb{D})$ is strongly dense in the set of all bounded linear operators ${\mathcal L}(L_a^{2, \mathbb{C}^n}(\mathbb{D}))$ and characterize all finite rank little Hankel operators.

Keywords

Bergman space

Toeplitz operators

little Hankel operators

strong-operator topology

finite rank operators

Subjects

• 46 Functional analysis
• 47 Operator theory

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