Results 11 to 20 of about 752 (101)
Algebras of frequently hypercyclic vectors [PDF]
Mathematische Nachrichten, 2019 We show that the multiples of the backward shift operator on the spaces $\ell_{p}$, $1\leq ...
Falcó, Javier, Grosse-Erdmann, Karl-G.
core +3 more sources
Linear Structure of Hypercyclic Vectors
Journal of Functional Analysis, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
León-Saavedra, Fernando +1 more
openaire +4 more sources
Fast orbital convergence reveals more hypercyclic vectors
Applied General TopologyLet X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a ...
T. K. Subrahmonian Moothathu
doaj +4 more sources
Hypercyclic and Cyclic Vectors
Journal of Functional Analysis, 1995 Let \(\mathcal X\) denote a separable complex Banach space. A vector \(x\in {\mathcal X}\) is said to be hypercyclic for an operator \(T\) on \(\mathcal X\) if the set \(\{T^n x: n\in \mathbb{N}\}\) is norm dense in \(\mathcal X\). We say that \(x\) is supercyclic if the set \(\{aT^n x: n\in \mathbb{N}, a\in \mathbb{C}\}\) is norm dense. An operator is
openaire +3 more sources
Perturbations of hypercyclic vectors
Journal of Mathematical Analysis and Applications, 2002 A bounded linear operator \(T\) on a separable Banach space \(\mathcal B\) is said to be hypercyclic if there is \(x \in \mathcal B\), also called hypercyclic, such that the elements in the orbit \(\{T^ n x\}_{n\geq 0}\) are dense in \(\mathcal B\). Hypercyclicity is one of the strongest forms of cyclicity. \textit{S. Rolewicz} [Stud. Math. 32, 17--22 (
openaire +3 more sources
Common hypercyclic vectors for the conjugate class of a hypercyclic operator
Journal of Mathematical Analysis and Applications, 2011 Let \(X\) be an infinite-dimensional, separable Banach space and \(B(X)\) the algebra of all bounded linear operators on \(X\). The authors show that, if \(T\) is a continuous hypercyclic operator on \(X\), then the conjugate set \(S(T):=\{L^{-1}TL: L\in B(X)\) invertible\} contains a path \(\{F_t\in B(X)\), \(t\in [1,\infty[\}\) of operators which is ...
Chan, Kit C., Sanders, Rebecca
openaire +3 more sources
Hypercyclic operators on topological vector spaces [PDF]
Journal of the London Mathematical Society, 2010 Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result.
Shkarin, Stanislav
core +2 more sources
Common hypercyclic vectors for the unitary orbit of a hypercyclic operator
Journal of Mathematical Analysis and Applications, 2012 The authors continue their recent work on common hypercyclic vectors for paths and similarity orbits of operators \(T\) on a separable Hilbert space \(H\) [J. Oper. Theory 61, 191--233 (2009); ibid. 66, No.~1, 107--124 (2011; Zbl 1230.47021); J. Math. Anal. Appl. 375, No.~1, 139--148 (2011; Zbl 1208.47013); Integral Equations Oper.
Chan, Kit C., Sanders, Rebecca
openaire +4 more sources
Common hypercyclic vectors for multiples of backward shift
Journal of Functional Analysis, 2003 We prove that the space $l^2$ contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1.
Abakumov, Evgeny, Gordon, J
openaire +6 more sources
Algebrability of the set of hypercyclic vectors for backward shift operators [PDF]
Advances in Mathematics, 2020 We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Fr chet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.
Falcó, Javier, Grosse-Erdmann, Karl-G.
openaire +6 more sources