Products of Toeplitz Operators on a Vector Valued Bergman Space

Robert Kerr

Products of Toeplitz Operators on a Vector Valued Bergman Space

Complex Variables 2008-04-29 v1 Functional Analysis

Authors: Robert Kerr

Abstract

We give a necessary and a sufficient condition for the boundedness of the Toeplitz product $T_FT_{G^*}$ on the vector valued Bergman space $L_a^2(\mathbb{C}^n)$ , where $F$ and $G$ are matrix symbols with scalar valued Bergman space entries. The results generalize existing results in the scalar valued Bergman space case. We also characterize boundedness and invertibility of Toeplitz products $T_FT_{G^*}$ in terms of the Berezin transform, generalizing results found by Zheng and Stroethoff for the scalar valued Bergman space.

Keywords

toeplitz operators bergman spaces tensor product

Cite

@article{arxiv.0804.4234,
  title  = {Products of Toeplitz Operators on a Vector Valued Bergman Space},
  author = {Robert Kerr},
  journal= {arXiv preprint arXiv:0804.4234},
  year   = {2008}
}