Composition operators on the Bloch space of the unit ball of a Hilbert space. (English) Zbl 1361.32024
Summary: Every analytic self-map of the unit ball of a Hilbert space induces a bounded composition operator on the space of Bloch functions. Necessary and sufficient conditions for compactness of such composition operators are provided, as well as some examples that clarify the connections among such conditions.
MSC:
32K05 | Banach analytic manifolds and spaces |
32A18 | Bloch functions, normal functions of several complex variables |
32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
47B33 | Linear composition operators |