HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
نویسندگان
چکیده
منابع مشابه
Hypercyclicity Criterion of Multiple Weighted Composition Operators
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
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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...
متن کاملSupercyclicity of Multiple Weighted Composition Operators
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}....
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(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2014
ISSN: 0304-9914
DOI: 10.4134/jkms.2014.51.2.363