Let ǫ > 0. A continuous linear operator T : C(X) −→ C(Y ) is said to be ǫ-disjointness preserving if ‖(Tf)(Tg)‖ ∞ ≤ ǫ, whenever f, g ∈ C(X) satisfy ‖f‖ ∞ = ‖g‖ ∞ = 1 and fg ≡ 0. In this paper we address basically two main questions: 1.How close there must be a weighted composition operator to a given ǫ-disjointness preserving operator? 2.How far can the set of weighted composition operators be ...

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...

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}....

The vector x is called supercyclic for T ifC orb T, x is dense inH. Also a supercyclic operator is one that has a supercyclic vector. For some sources on these topics, see 1–16 . Let H be a separable 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 repre...

In this paper we give some sufficient conditions for the adjoint of the multiple weighted composition operators acting on some function spaces satisfying the Hypercyclicity Criterion. Mathematics Subject Classification: 47B37; 47B33