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THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE

  • Lu, Yufeng ;
  • Cui, Puyu ;
  • Shi, Yanyue
  • Received : 2013.03.13
  • Published : 2014.01.31

Abstract

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.

Keywords

hyponormality;block Toeplitz operator;block Hankel operator

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  1. Hyponormality of Toeplitz operators in several variables by the weighted shifts approach pp.1563-5139, 2018, https://doi.org/10.1080/03081087.2018.1556241