Disk-cyclic and Codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert spaces

Liang, Yu-Xia; Zhou, Zehua

doi:10.36045/bbms/1464710114

Cited by 9 publications

(10 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By [38, page 36], ϕ is conjugate to a rotationφ, i.e., there exists a homeomorphism h : ∂D → ∂D such thatφ = h −1 • ϕ • h, and thus, C w,ϕ is similar to C w•h,φ [21]. Since C w•h,φ is not τ p -supercyclic by Proposition 24, then C w,ϕ is not τ p -supercyclic [27]. ✷ From all our results it seems natural to conjecture that if X is compact, E ֒→ (C(X), τ p ) is a Banach space and the operator C w,ϕ : E → E is isometric, then C w,ϕ is not τ psupercyclic.…”

Section: Lemma 22mentioning

confidence: 99%

Supercyclicity of weighted composition operators on spaces of continuous functions

2019

View full text Add to dashboard Cite

Our study is focused on the dynamics of weighted composition operators defined on a locally convex space E ֒→ (C(X), τ p ) with X being a topological Hausdorff space containing at least two different points and such that the evaluations {δ x : x ∈ X} are linearly independent in E ′ . We prove, when X is compact and E is a Banach space containing a nowhere vanishing function, that a weighted composition operator C w,ϕ is never weakly supercyclic on E. We also prove that if the symbol ϕ lies in the unit ball of A(D), then every weighted composition operator can never be τ psupercyclic neither on C(D) nor on the disc algebra A(D). Finally, we obtain Ansari-Bourdon type results and conditions on the spectrum for arbitrary weakly supercyclic operators, and we provide necessary conditions for a composition operator to be weakly supercyclic on the space of holomorphic functions defined in non necessarily simply connected planar domains. As a consequence, we show that no composition operator can be weakly supercyclic neither on the space of holomorphic functions on the punctured disc nor in the punctured plane.

show abstract

Section: Lemma 22mentioning

confidence: 99%

Supercyclicity of weighted composition operators on spaces of continuous functions

2019

View full text Add to dashboard Cite

show abstract

“…She studied some of their properties like the range of them, some necessarily and sufficient conditions to be 2 . In 2004, Leon-Saavedra and Muller, proved that every circle cyclic operator is hypercyclic, which mean ( , ) ≔ { : n ≥ 0} is dense in 3 , while the other kinds have been gaining importance in recent years such as Liang and Zhou 4,5 , Wong and Zeng 6 …etc.…”

Section: Introductionmentioning

confidence: 99%

On Hereditarily Codiskcyclic Operators

Jamil

2022

Baghdad Sci.J

View full text Add to dashboard Cite

Many codiskcyclic operators on infinite-dimensional separable Hilbert space do not satisfy the criterion of codiskcyclic operators. In this paper, a kind of codiskcyclic operators satisfying the criterion has been characterized, the equivalence between them has been discussed and the class of codiskcyclic operators satisfying their direct summand is codiskcyclic. Finally, this kind of operators is used to prove that every codiskcyclic operator satisfies the criterion if the general kernel is dense in the space.

show abstract

“…In the case of a separable complex Banach space, an operator T is codiskcyclic if and only if it is codisk transitive; that is for each pair (U, V ) of nonempty open sets there exist some α ∈ U and some n ≥ 0 such that αT n (U ) ∩ V = ∅. For a general overview of the codiskcyclicity, see [13,14,17,19].…”

Section: Introduction and Preliminarymentioning

confidence: 99%

Codiskcyclic sets of operators on complex topological vector spaces

Amouch¹,

Benchiheb²

2021

Preprint

View full text Add to dashboard Cite

Let X be a complex topological vector space and L(X) the set of all continuous linear operators on X. In this paper, we extend the notion of the codiskcyclicity of a single operator T ∈ L(X) to a set of operators Γ ⊂ L(X). We prove some results for codiskcyclic sets of operators and we establish a codiskcyclicity criterion. As an application, we study the codiskcyclicity of C 0 -semigroups of operators.2010 Mathematics Subject Classification. 47A16.

show abstract

Disk-cyclic and Codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert spaces

Abstract: Some sufficient conditions under which the tuple of the adjoint of weighted composition operators (C * ω 1 ,ϕ 1 , C * ω 2 ,ϕ 2 ) on the Hilbert space H of analytic functions is disk-cyclic (or codisk-cyclic) were investigated.

Cited by 9 publications

References 16 publications

Supercyclicity of weighted composition operators on spaces of continuous functions

Supercyclicity of weighted composition operators on spaces of continuous functions

On Hereditarily Codiskcyclic Operators

Codiskcyclic sets of operators on complex topological vector spaces

Contact Info

Product

Resources

About