Reflexivity on Banach Spaces of Analytic Functions

. Let X be a Banach space of functions analytic on a plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that X contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive

Weighted Sequence Spaces and Cyclicity

In this paper we investigate the cyclicity of the multiplication operator Mz acting on the weighted Hardy spaces of formal Laurent series. AMS Subject Classification: Primary 47B37; Secondary 47A16. Keywords and Phrases: Banach space of Laurent series associated with a sequence β, cyclic vector, multiplication operator, disc algebra

Supercyclicity with Respect to a Sequence on Special Sequence Spaces

Let {β(n)}∞ n=−∞ be a sequence of positive numbers such that β(0) = 1 and let 1 < p < ∞. We consider the space of all formal Laurent series f(z) = P∞ n=−∞ ˆf(n)z n such that X∞ n=−∞ | ˆf(n)| pβ(n) p < ∞. We investigate the supercyclicity with respect to a sequence on the Banach spaces of formal Laurent serie