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The Hyponormal Toeplitz operators on the vector valued Bergman space

Yanyue Shi|Yufeng Lu|Puyu Cui
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회보 (Bulletin of the KMS)|제51권 제1호|pp. 237-252

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키워드

hyponormalityblock Toeplitz operatorblock Hankel operator
주제분류수학

초록

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ ∈ h∞ ⓧ Mn×n on L2 a(D, Cn).

Abstract

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ 2 h∞ ⓧ Mn×n on L2 a(D, Cn).

참고문헌 (12)

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  7. In Sung Hwang, "HYPONORMAL TOEPLITZ OPERATORS ON THE BERGMAN SPACE", 대한수학회지, 42(2), pp.197~213 (2005), 대한수학회
  8. I. S. Hwang, "Hyponormality of trigonometric Toeplitz operators", Trans. Amer. Math. Soc, 354(6), pp.2461~2474 (2002)
  9. 황인성, "Hyponormal Toeplitz operators on the Bergman space. II.", 대한수학회보, 44(3), pp.517~522 (2007), 대한수학회
  10. Y. F. Lu, "Hyponormal Toeplitz operators on the weighted Bergman space", Integral Equations Operator Theory, 65, pp.115~129 (2009)
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관련 논문AI추천

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