Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE TOEPLITZ OPERATOR INDUCED BY AN R-LATTICE

  • Kang, Si Ho (Department of Mathematics Sookmyung Women's University)
  • Published : 2012.08.15
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Abstract

The hyperbolic metric is invariant under the action of M$\ddot{o}$bius maps and unbounded. For 0 < $r$ < 1, there is an r-lattice in the Bergman metric. Using this r-lattice, we get the measure ${\mu}_r$ and the Toeplitz operator $T^{\alpha}_{\mu}_r$ and we prove that $T^{\alpha}_{\mu}_r$ is bounded and $T^{\alpha}_{\mu}_r$ is compact under some condition.

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References

  1. S. Axler, Bergman Spaces and Their operators, Pitman Research Notes in Mathematics, vol. 171, 1-50, Longman, Harlow.
  2. S. Axler and D. Zheng, Compact operators via the Berezin Transform, Indiana Univ. Math. 47 (1988), 387-399.
  3. K. H. Zhu, Hankel-Toeplitz type operators on $L^1_a(\Omega)$ , Integral Equations and operator Theory 13 (1990), 285-302. https://doi.org/10.1007/BF01193761
  4. K. Zhu, Operator Theory in Function Spaces, 2ed., American Mathematical Society, 2007.