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Unbounded Weighted Composition Operators on Fock space

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Abstract

In this paper, we consider unbounded weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as \(\mathcal {C}\)-selfadjoint (with respect to weighted composition conjugations), Hermitian, normal, and cohyponormal. In addition, the paper shows that unbounded normal weighted composition operators are contained properly in the class of \(\mathcal {C}\)-selfadjoint operators with respect to weighted composition conjugations.

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Acknowledgments

The author wishes to thank Dr L. H. Khoi for a comment on the presentation of the first draft. The author also greatly appreciates the careful eye of the anonymous referee, who pointed out minor typos in Theorem 3.3.

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  1. ISE Department at the National University of Singapore (NUS), 117576, Singapore, Singapore

    Pham Viet Hai

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  1. Pham Viet Hai
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Correspondence to Pham Viet Hai.

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Hai, P. Unbounded Weighted Composition Operators on Fock space. Potential Anal 53, 1–21 (2020). https://doi.org/10.1007/s11118-018-09757-5

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