Research article

Self-adjoint and hyponormal weighted composition operators on the Fock space

  • Received: 01 July 2024 Revised: 02 August 2024 Accepted: 14 August 2024 Published: 27 August 2024
  • MSC : 47B32, 47A10

  • One major aim of this paper is to characterize the self-adjointness of some special weighted composition operators on Fock space, and another major aim is to characterize the hyponormality of some composition operators on such space.

    Citation: Zhi-jie Jiang. Self-adjoint and hyponormal weighted composition operators on the Fock space[J]. AIMS Mathematics, 2024, 9(9): 24989-24997. doi: 10.3934/math.20241218

    Related Papers:

  • One major aim of this paper is to characterize the self-adjointness of some special weighted composition operators on Fock space, and another major aim is to characterize the hyponormality of some composition operators on such space.



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    [1] H. B. Bai, Z. J. Jiang, X. B. Hu, Z. A. Li, 2-complex symmetric weighted composition operators on Fock space, AIMS Math., 8 (2023), 21781–21792. http://dx.doi.org/10.3934/math.20231111 doi: 10.3934/math.20231111
    [2] S. R. Bhuia, A class of $C$-normal weighted composition operators on Fock space $\mathcal{F}^2({\mathbb C})$, J. Math. Anal. Appl., 508 (2022), 125896. http://dx.doi.org/10.1016/j.jmaa.2021.125896 doi: 10.1016/j.jmaa.2021.125896
    [3] B. J. Carswell, B. D. MacCluer, A. Schuster, Composition operators on the Fock space, Acta Sci. Math. (Szeged), 69 (2003), 871–887.
    [4] C. C. Cowen, E. A. Gallardo-Gutiérrez, A new class of operators and a description of adjoints of composition operators, J. Funct. Anal., 238 (2006), 447–462. http://dx.doi.org/10.1016/j.jfa.2006.04.031 doi: 10.1016/j.jfa.2006.04.031
    [5] K. W. Dennis, Co-hyponormality of composition operators on the Hardy spaces, Michigan: Michigan University, 2000.
    [6] R. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math.Soc., 17 (1966), 413–416. http://dx.doi.org/10.2307/2035178 doi: 10.2307/2035178
    [7] L. X. Feng, L. K. Zhao, A class of weighted composition operators on the Fock space, Complex. Var. Elliptic. Equ., 65 (2020), 1001–1017. http://dx.doi.org/10.1080/17476933.2019.1643332 doi: 10.1080/17476933.2019.1643332
    [8] F. Forelli, The isometries on $H^p$, Canadian J. Math., 16 (1964), 721–728.
    [9] P. R. Halmos, A Hilbert space problem book, New York: Springer Press, 1982. http://dx.doi.org/10.1007/978-1-4684-9330-6
    [10] T. Le, Normal and isometric weighted composition operators on the Fock space, Bull. London Math. Soc., 46 (2014), 847–856. http://dx.doi.org/10.1112/blms/bdu046 doi: 10.1112/blms/bdu046
    [11] P. T. Tien, L. H. Khoi, Weighted composition operators between different Fock spaces, Potential. Anal., 50 (2017), 171–195. https://doi.org/10.48550/arXiv.1704.03752 doi: 10.48550/arXiv.1704.03752
    [12] H. Sadraoui, Hyponormality of Toeplitz operators and composition operators, City of West Lafayette: Purdue University, 1992.
    [13] S. Ueki, Weighted composition operator on the Fock space, Proc. Amer. Math. Soc., 135 (2007), 1405–1410. https://doi.org/10.1090/s0002-9939-06-08605-9 doi: 10.1090/s0002-9939-06-08605-9
    [14] L. Zhao, Unitary weighted composition operators on the Fock space of $ {\mathbb C}^N$, Complex Anal. Oper. Theory., 8 (2014), 581–590. https://doi.org/10.1007/s11785-013-0313-7 doi: 10.1007/s11785-013-0313-7
    [15] L. Zhao, A class of normal weighted composition operators on the Fock space of $ {\mathbb C}^N$, Acta Math. Sin., 31 (2015), 1789–1797. https://doi.org/10.1007/s10114-015-4758-7 doi: 10.1007/s10114-015-4758-7
    [16] L. Zhao, Invertible weighted composition operators on the Fock space of $ {\mathbb C}^N$, J. Funct. Space., 2015 (2015), 250358. https://doi.org/10.1155/2015/250358 doi: 10.1155/2015/250358
    [17] K. H. Zhu, Analysis on Fock spaces, New York: Springer Press, 2012. https://doi.org/10.1007/978-1-4419-8801-0_1
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