Supercyclicity of Multiple Weighted Composition Operators
نویسندگان
چکیده
Let H be a Hilbert space of functions analytic on a plane domain G such that for each λ in G the linear functional of evaluation at λ given by f −→ f(λ) is a bounded linear functional on H . By the Riesz representation theorem there is a vector Kλ in H such that f(λ) =< f,Kλ >. Let T = (T1, T2) be the pair of commutative bounded linear operators T1 and T2 acting on H . Put F = {T1T2 : m,n ≥ 0}. For x ∈ H , the orbit of x under T is the set orb(T, x) = {Sx : S ∈ F}. The vector x is called hypercyclic for T if orb(T, x) is dense in H . Also, the vector x is called supercyclic for T if Corb(T, x) is dense in H . Supercyclicity was introduced by Hilden and Wallen ([1]). They showed that all unilateral backward weighted shifts are supercyclic, but there is no vector that is supercyclic vector for all the unilateral backward weighted shifts. H. Salas ([2]) give a condition for supercyclicity in Frechet spaces which is called the Supercyclicity Criterion.
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