Toeplitz and Hankel Operators on a Vector-valued Bergman Space

Document Type: Original Article


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


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.


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