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Weighted composition groups on the little Bloch space. (English) Zbl 1437.47019

Summary: We determine both the semigroup and spectral properties of a group of weighted composition operators on the little Bloch space. It turns out that these are strongly continuous groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the infinitesimal generator as well as the resulting resolvents which are given as integral operators. As a consequence, we complete the analysis of the adjoint composition group on the predual of the nonreflexive Bergman space and a group of isometries associated with a specific automorphism of the upper half-plane.

MSC:

47D03 Groups and semigroups of linear operators
47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
30H30 Bloch spaces
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References:

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