Results 31 to 40 of about 216 (102)
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We prove some further properties of the operator T ∈ [nQN] (n‐power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator T ∈ [nQN] satisfying the translation invariant property is normal and that the operator T ∈ [nQN] is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator T ∈ [
Sid Ahmed Ould Ahmed Mahmoud +1 more
wiley +1 more source
Denseness of sets of supercyclic vectors [PDF]
Mathematical Proceedings of the Royal Irish Academy, 2020 The sets of strongly supercyclic, weakly l-sequentially supercyclic, weakly sequentially supercyclic, and weakly supercyclic vectors for an arbitrary normed-space operator are all dense in the normed space, regardless the notion of denseness one is considering, provided they are nonempty.
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Cyclicity of composition operators on the Fock space [PDF]
, 2022 In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type of operators.
Bayart, Frédéric +1 more
core +2 more sources
On supercyclicity of operators from a supercyclic semigroup
Journal of Mathematical Analysis and Applications, 2011 We show that for every supercyclic strongly continuous operator semigroup ${T_t}_{t\geq 0}$ acting on a complex $\F$-space, every $T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic vectors of each $T_t$ with $t>0$ is exactly the set of supercyclic vectors of the entire semigroup.
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On Some Subspace Codiskcyclic Operators in Banach Spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This paper introduces the concepts of subspace codiskcyclicity and subspace codisk transitivity, providing criteria and examples that highlight their distinct properties compared to traditional codiskcyclic operators and hypercyclic operators. The paper also demonstrates the existence of subspace codiskcyclic operators in finite‐dimensional Banach ...
Peter Masong Slaa +3 more
wiley +1 more source
Hypercyclic tuples of operators on $C^n$ and $R^n$ [PDF]
, 2012 A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$.
Shkarin, Stanislav
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Dynamics, Operator Theory, and Infinite Holomorphy
, 2014 Abstract and Applied Analysis, Volume 2014, Issue 1, 2014.
Alfred Peris +3 more
wiley +1 more source
The role of the angle in supercyclic behavior
Journal of Functional Analysis, 2003 A (bounded) operator \(T\) on a complex infinite dimensional separable Hilbert space \(H\) is said to be supercyclic if there is a (supercyclic) vector \(x \in X\) such that its projective orbit \(\{\lambda T^n(x) : n \in \mathbb{N}\), \(\lambda \in \mathbb{C} \}\) is dense in \(H\). One of the ideas of \textit{A. Montes-Rodríguez} and \textit{H.
Gallardo-Gutiérrez, Eva A. +1 more
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Cyclic behaviour of Volterra composition operators [PDF]
, 2011 We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$,where $?$ is a measurable self-map of [0, 1].
Stanislav Shkarin +5 more
core +1 more source
Weak l-sequential supercyclicity and weak quasistability [PDF]
It is known that supercyclicity implies strong stability. It is not known whether weak l-sequential supercyclicity implies weak stability. In this paper we prove that weak l-sequential supercyclicity implies weak quasistability.
Duggal, B. P., Kubrusly, C. S.
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