Semigroups of composition operators on vector-valued Hardy spaces. (English) Zbl 1509.47061
The authors show the existence of a one-to-one correspondence between the set of all semigroups of holomorphic self-mappings of the upper-half plane and the set of of all strongly continuous semigroups of composition operators on the vector-valued Hardy space of the upper-half plane.
Reviewer: Pham Viet Hai (Hanoi)
MSC:
| 47D03 | Groups and semigroups of linear operators |
| 47B33 | Linear composition operators |
| 46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
| 46B50 | Compactness in Banach (or normed) spaces |
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