Order-Bounded Difference in Weighted Composition Operators Between Fock Spaces

Xiao-Feng Peng and Zhi-Jie Jiang ()
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Xiao-Feng Peng: School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Zhi-Jie Jiang: School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China

Mathematics, 2024, vol. 12, issue 21, 1-18

Abstract: There are two aims in this paper. The first aim is to characterize the order-bounded weighted composition operators between Fock spaces, and the second is to further characterize the order-bounded difference in weighted composition operators between Fock spaces. At the same time, six examples are given to illustrate the relations between boundedness and ordered boundedness. Moreover, an interesting result is found that differences in weighted composition operators defined by some special weighted functions and symbol functions are order-bounded between Fock spaces if and only if each weighted composition operator is compact between Fock spaces. Finally, two open questions are also put forward for converting larger Fock spaces into smaller ones.

Keywords: weighted composition operator; Fock space; order-boundedness; compactness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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