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Volume 31, Issue 3
A Note on Weighted Composition Operators on the Fock Space

Lixia Feng & Liankuo Zhao

DOI: 10.13447/j.1674-5647.2015.03.11

Commun. Math. Res., 31 (2015), pp. 281-284.

Published online: 2021-05

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  • Abstract

Based on a new characterization of bounded and compact weighted composition operators on the Fock space obtained by Le T (Le T. Normal and isometric weighted composition operators on the Fock space. Bull. London. Math. Soc., 2014, 46: 847–856), this paper shows that a bounded weighted composition operator on the Fock space is a Fredholm operator if and only if it is an invertible operator, and if and only if it is a nonzero constant multiple of a unitary operator. The result is very different from the corresponding results on the Hardy space and the Bergman space.

  • Keywords

Fock space, weighted composition operator, Fredholm, invertible, unitary.

  • AMS Subject Headings

47B32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-281, author = {Feng , Lixia and Zhao , Liankuo}, title = {A Note on Weighted Composition Operators on the Fock Space}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {3}, pages = {281--284}, abstract = {

Based on a new characterization of bounded and compact weighted composition operators on the Fock space obtained by Le T (Le T. Normal and isometric weighted composition operators on the Fock space. Bull. London. Math. Soc., 2014, 46: 847–856), this paper shows that a bounded weighted composition operator on the Fock space is a Fredholm operator if and only if it is an invertible operator, and if and only if it is a nonzero constant multiple of a unitary operator. The result is very different from the corresponding results on the Hardy space and the Bergman space.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.03.11}, url = {http://global-sci.org/intro/article_detail/cmr/18930.html} }
TY - JOUR T1 - A Note on Weighted Composition Operators on the Fock Space AU - Feng , Lixia AU - Zhao , Liankuo JO - Communications in Mathematical Research VL - 3 SP - 281 EP - 284 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.03.11 UR - https://global-sci.org/intro/article_detail/cmr/18930.html KW - Fock space, weighted composition operator, Fredholm, invertible, unitary. AB -

Based on a new characterization of bounded and compact weighted composition operators on the Fock space obtained by Le T (Le T. Normal and isometric weighted composition operators on the Fock space. Bull. London. Math. Soc., 2014, 46: 847–856), this paper shows that a bounded weighted composition operator on the Fock space is a Fredholm operator if and only if it is an invertible operator, and if and only if it is a nonzero constant multiple of a unitary operator. The result is very different from the corresponding results on the Hardy space and the Bergman space.

Feng , Lixia and Zhao , Liankuo. (2021). A Note on Weighted Composition Operators on the Fock Space. Communications in Mathematical Research . 31 (3). 281-284. doi:10.13447/j.1674-5647.2015.03.11
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