Khoi, Le Hai; Thom, Le Thi Hong; Tien, Pham Trong Weighted composition operators between Fock spaces \(\mathcal{F}^\infty(\mathbb C)\) and \(\mathcal{F}^p(\mathbb C)\). (English) Zbl 07047452 Int. J. Math. 30, No. 3, Article ID 1950015, 16 p. (2019). Summary: In this paper, we establish necessary and sufficient conditions for boundedness and compactness of weighted composition operators acting between Fock spaces \(\mathcal{F}^\infty(\mathbb C)\) and \(\mathcal{F}^p(\mathbb C)\). We also give complete descriptions of path connected components for the space of composition operators and the space of nonzero weighted composition operators in this context. Cited in 5 Documents MSC: 47B33 Linear composition operators 30D15 Special classes of entire functions of one complex variable and growth estimates Keywords:Fock space; weighted composition operator; topological structure PDFBibTeX XMLCite \textit{L. H. Khoi} et al., Int. J. Math. 30, No. 3, Article ID 1950015, 16 p. (2019; Zbl 07047452) Full Text: DOI References: [1] Bonet, J., Domański, P., Lindström, M. and Taskinen, J., Composition operators between Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A64 (1998) 101-118. · Zbl 0912.47014 [2] Carswell, B., MacCluer, B. and Schuster, A., Composition operators on the Fock space, Acta Sci. Math.69 (2003) 871-887. · Zbl 1051.47023 [3] Chalendar, I., Gallardo-Gutierrez, E. A. and Partington, J. R., Weighted composition operators on the Dirichlet space: Boundedness and spectral properties, Math. Ann.363 (2015) 1265-1279. · Zbl 1390.47004 [4] Contreras, M. D. and Hernández-Díaz, A. G., Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A69 (2000) 41-60. · Zbl 0990.47018 [5] Izuchi, K. J. and Ohno, S., Path connected components in weighted composition operators on \(h^\infty\) and \(H^\infty\) with the operator norm, Trans. Amer. Math. Soc.365 (2013) 3593-3612. · Zbl 1282.47048 [6] MacCluer, B. and Shapiro, J., Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Can. J. Math.38 (1986) 878-906. · Zbl 0608.30050 [7] Mengestie, T., Volterra type and weighted composition operators on weighted Fock spaces, Integr. Equ. Oper. Theory76 (2013) 81-94. · Zbl 1296.47030 [8] Shapiro, J. H. and Sundberg, C., Isolation amongst the composition operators, Pacific J. Math.145 (1990) 117-152. · Zbl 0732.30027 [9] Tien, P. T. and Khoi, L. H., Weighted composition operators between different Fock spaces, Potential Anal.50 (2019) 171-195. · Zbl 1411.30040 [10] Ueki, S., Weighted composition operators on some function spaces of entire functions, Bull. Belg. Math. Soc. Simon Stevin17 (2010) 343-353. · Zbl 1191.47032 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.