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Products of Volterra Type Operators and Composition Operators Between Fock Spaces

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Abstract

We show that entire functions \(\varphi \), which induce bounded products of Volterra integral operators \(V_g\) (Volterra companion operators \(J_g\)) and composition operators \(C_{\varphi }\) acting between different Fock spaces, must be affine functions, i.e. \(\varphi (z) = az + b\). Then, using this special form of \(\varphi \), we characterize boundedness and compactness of these products in term of new quantities, which are much simpler than the Berezin type integral transforms in the previous papers.

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Acknowledgements

The author is deeply grateful to the Referee for useful remarks and comments that led to the improvement of the paper. This article has been carried out during the author’s stay at the Vietnam Institute for Advanced Study in Mathematics. He would like to thank the institution for hospitality and support.

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Authors and Affiliations

  1. Faculty of Mathematics, Mechanics and Informatics, University of Science, Vietnam National University, Hanoi, Vietnam

    Pham Trong Tien

  2. Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Pham Trong Tien

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  1. Pham Trong Tien
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Correspondence to Pham Trong Tien.

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Dedicated to my supervisor Prof. Alexander V. Abanin on the occasion of his 65th birthday

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Tien, P.T. Products of Volterra Type Operators and Composition Operators Between Fock Spaces. Results Math 75, 104 (2020). https://doi.org/10.1007/s00025-020-01222-3

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  • DOI: https://doi.org/10.1007/s00025-020-01222-3

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