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We discuss the frequent hypercyclicity and hypercyclicity of multiples of the linear fractional composition operators on Aαp and give equivalent conditions of the frequent hypercyclicity and hypercyclicity. We also characterize disjoint hypercyclicity and disjoint mixing behavior of finitely many linear fractional composition operators on the weighted Bergman spaces Aαp.
We study the degree of compactness of composition operators Cφ acting on weighted Hilbert spaces of entire functions, which include (i) the space of entire Dirichlet series, (ii) the space of entire power series, and (iii) the Fock space (we must have φ(z)=az+b, and it is known that Cφ is compact if and only if |a|<1). More precisely, the sequence (an) of approximation numbers of Cφ is investigated:...
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