Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Class of Normaloid Weighted Composition Operators on the Fock Space over ℂ

  • Received : 2020.08.20
  • Accepted : 2021.02.08
  • Published : 2021.12.31
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Abstract

Let 𝜙 be an entire self map on ℂ and let 𝜓 be an entire function on ℂ. A weighted composition operator induced by 𝜙 with weight 𝜓 is given by C𝜓,𝜙. In this paper we investigate under what conditions the weighted composition operators C𝜓,𝜙 on the Fock space over ℂ induced by 𝜙 with weight of the form $k_c({\zeta})=e^{{\langle}{\zeta},c{\rangle}-{\frac{{\mid}c{\mid}^2}{2}}}$ is normaloid and essentially normaloid.

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References

  1. B. J. Carswell, B. D. MacCluer and A. Schuster, Composition Operators on the Fock Space, Acta. Sci. Math. (Szeged)., (69)(2003), 871-887.
  2. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytical Functions, Studies in Advanced Mathematics, CRC Press.
  3. J. Dai, The Norm of Composition Operators on the Fock Space, Complex Variables and Elliptic Equations, (64)(9)(2019), 1-9. https://doi.org/10.1080/17476933.2017.1409740
  4. K. Guo and K. Izuchi, Composition Opertors on Fock Type Spaces, Acta Sci. Math.(Szeged)., (74)(3-4)(2008), 807-828.
  5. K. E. Gustafson and K. M. Rao, Numerical Range, Springer-Verlag New York, 1997.
  6. T. Le, Normal and Isometric Weighted Composition Operators on the Fock Space, Bull. Lond. Math. Soc., (46)(4)(2014), 847-856. https://doi.org/10.1112/blms/bdu046
  7. V. Matache, Numerical Range of Composition Operators, Linear. Algebra. Appl., (331)(2001), 61-74. https://doi.org/10.1016/S0024-3795(01)00262-2
  8. T. Mengestie and W. Seyoum, Spectra of Composition Operators on Fock-type Spaces, Questiones Mathematicae, (2019), 1-16.
  9. J. H. Shapiro, Composition Operators and Classical Tunction Theory, Universitext: Tracts in Mathematics, Springer - Verlag, New York, 1993.
  10. D. Thompson, Normaloid Weighted Composition Operators on ℋ2, J. Math. Anal. Appl., (467)(2)(2018), 1153-1162. https://doi.org/10.1016/j.jmaa.2018.07.061
  11. L. Zhao, Unitary Weighted Composition Operator on the Fock Space of ℂn, Complex. Anal. Oper. Theory., (8)(2)(2014), 581-590. https://doi.org/10.1007/s11785-013-0313-7
  12. K. Zhu, Analysis on Fock Spaces, Graduate Text in Mathematics, Springer, New York.