Results 11 to 20 of about 893 (111)
The Strong Disjoint Blow-Up/Collapse Property
Journal of Function Spaces and Applications, 2013 Let be a topological vector space, and let be the algebra of continuous linear operators on . The operators are disjoint hypercyclic if there is such that the orbit is dense in .
Héctor N. Salas
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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 (
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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
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Existence of Hypercyclic Operators on Topological Vector Spaces
Journal of Functional Analysis, 1997 The author establishes the following result: Suppose \(X\) is a topological vector space with a bounded biorthogonal system \(\{x_n, f_n\}\). Suppose \(X\) is \(\ell^1\)-complete with respect to \((x_n)\). (a) If \(\widetilde T: X\to X\) is continuous and \(\widetilde T(x_n)= w_nx_{n-1}\) for some bounded sequence \((w_n)\) of positive real numbers ...
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Non‐Diskcyclicity of Bounded Composition Operators on the Little Bloch Space and the Besov Space
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, we show that there are no diskcyclic composition operators on the little Bloch space ℬ0 and the Besov spaces Bp.
Hang Zhou +2 more
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On the Recurrent C0‐Semigroups, Their Existence, and Some Criteria
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, recurrent C0‐semigroups are introduced and investigated. It is proved that, despite hypercyclic C0‐semigroups, recurrent C0‐semigroups can be found on finite‐dimensional Banach spaces. Some criteria are stated for recurrence, which is based on open sets, neighborhoods of zero, and special eigenvectors.
Mansooreh Moosapoor, Tuncer Acar
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Topological Transitivity of Shift Similar Operators on Nonseparable Hilbert Spaces
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 In this paper, we investigate topological transitivity of operators on nonseparable Hilbert spaces which are similar to backward weighted shifts. In particular, we show that abstract differential operators and dual operators to operators of multiplication in graded Hilbert spaces are similar to backward weighted shift operators.
Andriy Zagorodnyuk +2 more
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Invariant Manifolds of Hypercyclic Vectors [PDF]
Proceedings of the American Mathematical Society, 1993 We show that any hypercyclic operator on Hilbert space has a dense, invariant linear manifold consisting, except for zero, entirely of hypercyclic vectors.
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Dynamics of tuples of matrices [PDF]
, 2008 In this article we answer a question raised by N. Feldman in \cite{Feldman} concerning the dynamics of tuples of operators on $\mathbb{R}^n$. In particular, we prove that for every positive integer $n\geq 2$ there exist $n$ tuples $(A_1, A_2, ..., A_n ...
Costakis, George +2 more
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Algebrable sets of hypercyclic vectors for convolution operators [PDF]
Israel Journal of Mathematics, 2020 We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff's operator also has this property on the space of complex-valued smooth functions on the real line.
Bès, Juan, Papathanasiou, Dimitris
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