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Let be a sequence of positive numbers and . We consider the space of all power series such that . We investigate strict cyclicity of , the weakly closed algebra generated by the operator of multiplication by acting on , and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on when is strictly cyclic.
In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.
Let be the Hilbert space with reproducing kernel . This paper characterizes some sufficient conditions for a sequence to be a universal interpolating sequence for .
The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small...
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