Some characterizations for composition operators on the Fock spaces. (English) Zbl 1368.47022
Summary: We study composition operators on the Fock spaces \(\mathcal{F}_\alpha^2(\mathbb{C}^n)\) for \(\alpha > 0\), problems considered including the essential norm, normality, spectra, cyclicity and membership in the Schatten classes. We give perfect characterizations for these basic properties, which are different with those composition operators on the Hardy space and the weighted Bergman spaces.
MSC:
| 47B33 | Linear composition operators |
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
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