Abstract
A left linear weighted composition operator \(W_{f,\varphi }\) is defined on slice regular quaternionic Fock space \(\mathcal {F}^2(\mathbb {H})\). We carry out a comprehensive analysis on its classical properties. Firstly, the boundedness and compactness of weighted composition operator on \(\mathcal {F}^2(\mathbb {H})\) are investigated systematically, which can be seen new and brief characterizations. And then all normal bounded weighted composition operators are found, particularly, equivalent conditions for self-adjoint weighted operators on \(\mathcal {F}^2(\mathbb {H})\) are developed. Finally, we describe all types of isometric weighted composition operators on \(\mathcal {F}^2(\mathbb {H})\).
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Acknowledgements
Y. X. Liang is supported by the National Natural Science Foundation of China (Grant No. 11701422).
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Liang, YX. A Left Linear Weighted Composition Operator on Quaternionic Fock Space. Results Math 74, 23 (2019). https://doi.org/10.1007/s00025-018-0948-9
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DOI: https://doi.org/10.1007/s00025-018-0948-9