| Abstrakt: |
A bounded linear operator Tacting on a Hilbert space His said to be recurrent if for every non-empty open subset U⊂Hthere is an integer nsuch that Tn(U)∩U≠∅. In this paper, we completely characterize the recurrence of scalar multiples of composition operators, induced by linear fractional self maps of the unit disk, acting on weighted Dirichlet spaces Sν; in particular on the Bergman space, the Hardy space, and the Dirichlet space. Consequently, we complete previous work of Costakis, Manoussos, and Parissis on the recurrence of linear fractional composition operators on Hardy space. In this manner, we determine the triples (λ,ν,ϕ)∈C×R×LFM(D)for which the scalar multiple of composition operator λCϕacting on Sνfails to be recurrent. |
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