Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE

  • Lu, Yufeng (School of Mathematical Sciences Dalian University of Technology) ;
  • Cui, Puyu (School of Mathematical Sciences Dalian University of Technology) ;
  • Shi, Yanyue (School of Mathematical Sciences Ocean University of China)
  • Received : 2013.03.13
  • Published : 2014.01.31
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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 $L^2_a(\mathbb{D},\mathbb{C}^n)$.

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References

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