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.
Das, N. (2015). Toeplitz and Hankel Operators on a Vector-valued Bergman Space. Khayyam Journal of Mathematics, 1(2), 230-242. doi: 10.22034/kjm.2015.13167
MLA
Namita Das. "Toeplitz and Hankel Operators on a Vector-valued Bergman Space". Khayyam Journal of Mathematics, 1, 2, 2015, 230-242. doi: 10.22034/kjm.2015.13167
HARVARD
Das, N. (2015). 'Toeplitz and Hankel Operators on a Vector-valued Bergman Space', Khayyam Journal of Mathematics, 1(2), pp. 230-242. doi: 10.22034/kjm.2015.13167
VANCOUVER
Das, N. Toeplitz and Hankel Operators on a Vector-valued Bergman Space. Khayyam Journal of Mathematics, 2015; 1(2): 230-242. doi: 10.22034/kjm.2015.13167