@article { author = {Das, Namita}, title = {Toeplitz and Hankel Operators on a Vector-valued Bergman Space}, journal = {Khayyam Journal of Mathematics}, volume = {1}, number = {2}, pages = {230-242}, year = {2015}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {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}, url = {https://www.kjm-math.org/article_13167.html}, eprint = {https://www.kjm-math.org/article_13167_cd3e86baa83715a9bf967ed60c149d34.pdf} }