Chaos for functions of discrete and continuous weighted shift operators

deLaubenfels, Ralph; Emamirad, Hassan

doi:10.1017/s0143385701001675

Cited by 54 publications

(50 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that if f λ = (1, λ, λ 2 , ...) and |λ| < 1, then ϕ(B)f λ = ϕ(λ)f λ . In [9], R. Delaubenfels and H. Emamirad proved that if ϕ(D) ∩ S 1 = φ, then ϕ(B) is hypercyclic on ℓ p . We now have the following result, which can be proved using Proposition 5.1.…”

Section: Q-frequent Hypercyclicity In S P (H)mentioning

confidence: 99%

q-Frequent hypercyclicity in spaces of operators

Gupta

Mundayadan

2016

Monatsh Math

View full text Add to dashboard Cite

Abstract. We provide conditions for a linear map of the form CR,T (S) = RST to be q-frequently hypercyclic on algebras of operators on separable Banach spaces. In particular, if R is a bounded operator satisfying the q-Frequent Hypercyclicity Criterion, then the map CR(S)=RSR * is shown to be q-frequently hypercyclic on the space K(H) of all compact operators and the real topological vector space S(H) of all self-adjoint operators on a separable Hilbert space H. Further we provide a condition for CR,T to be q-frequently hypercyclic on the Schatten von Neumann classes Sp(H). We also characterize frequent hypercyclicity of CM * ϕ ,M ψ on the trace-class of the Hardy space, where the symbol Mϕ denotes the multiplication operator associated to ϕ.

show abstract

Section: Q-frequent Hypercyclicity In S P (H)mentioning

confidence: 99%

q-Frequent hypercyclicity in spaces of operators

Gupta

Mundayadan

2016

Monatsh Math

View full text Add to dashboard Cite

show abstract

“…The following theorem was inspired by deLaubenfels and Emamirad [3], and its proof uses an argument of [7].…”

Section: Theorem 12]) a Hypercyclic Operator T Is Called Chaotic mentioning

confidence: 99%

On chaotic 𝐶₀-semigroups and infinitely regular hypercyclic vectors

Kalmes¹

2006

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. A C 0 -semigroup T = (T (t)) t≥0 on a Banach space X is called hypercyclic if there exists an element x ∈ X such that {T (t)x; t ≥ 0} is dense in X. T is called chaotic if T is hypercyclic and the set of its periodic vectors is dense in X as well. We show that a spectral condition introduced by Desch, Schappacher and Webb requiring many eigenvectors of the generator which depend analytically on the eigenvalues not only implies the chaoticity of the semigroup but the chaoticity of every T (t), t > 0. Furthermore, we show that semigroups whose generators have compact resolvent are never chaotic. In a second part we prove the existence of hypercyclic vectors in D(A ∞ ) for a hypercyclic semigroup T , where A is its generator.

show abstract

“…By strengthening the condition and analogous arguments, we also characterise topologically mixing weighted translation operators on discrete homogeneous spaces. Hypercyclcity in weighted L p spaces has also been studied in [16,17]. We will make use of the following form of the hypercyclic criterion in [8], derived from the original one obtained by Kitai [23], and by Gethner and Shapiro [19] independently.…”

Section: Introductionmentioning

confidence: 99%

Hypercyclicity of weighted convolution operators on homogeneous spaces

Chen

Chu

2009

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let 1 ≤ p < ∞. We show that a weighted translation operator on the L p space of a homogeneous space is hypercyclic under some condition on the weight. This condition is also necessary in the discrete case and is equivalent to hereditary hypercyclicity of the operator. The condition can be strengthened to characterise topologically mixing weighted translation operators on discrete spaces.

show abstract

Chaos for functions of discrete and continuous weighted shift operators

Cited by 54 publications

References 7 publications

q-Frequent hypercyclicity in spaces of operators

q-Frequent hypercyclicity in spaces of operators

On chaotic 𝐶₀-semigroups and infinitely regular hypercyclic vectors

Hypercyclicity of weighted convolution operators on homogeneous spaces

Contact Info

Product

Resources

About