Results 21 to 30 of about 98 (84)
Perturbation of m‐Isometries by Nilpotent Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We prove that if T is an m‐isometry on a Hilbert space and Q an n‐nilpotent operator commuting with T, then T + Q is a (2n + m − 2)‐isometry. Moreover, we show that a similar result for (m, q)‐isometries on Banach spaces is not true.
Teresa Bermúdez +4 more
wiley +1 more source
The Strong Disjoint Blow‐Up/Collapse Property
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 Let X be a topological vector space, and let ℬ(X) be the algebra of continuous linear operators on X . The operators T1, …, TN ∈ ℬ(X) are disjoint hypercyclic if there is x ∈ X such that the orbit {(T1n(x),…,TNn(x)):n∈ℕ} is dense in X × …×X . Bès and Peris have shown that if T1, …, TN satisfy the Disjoint Blow‐up/Collapse property, then they are ...
Héctor N. Salas, Ajda Fošner
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On the Existence of Polynomials with Chaotic Behaviour
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite‐dimensional separable Frèchet space admits mixing (hence hypercyclic) polynomials of arbitrary positive degree.
Nilson C. Bernardes Jr. +2 more
wiley +1 more source
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
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
Disjoint Supercyclic Weighted Shifts
Integral Equations and Operator Theory, 2016 Let \(T_1, \dots, T_N\) be \(N\) continuous linear operators acting on the same topological vector space \(X\). They are said to be disjoint hypercyclic (respectively, disjoint supercyclic) or \(d\)-hypercyclic (respectively, \(d\)-supercyclic) if there exists a vector \(x\) in \(X\) such that the vector \((x,\dots, x)\) is a hypercyclic vector ...
Martin, Özgür, Sanders, Rebecca
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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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TUPLES OF OPERATORS AND SUPERCYCLICITY [PDF]
International Journal of Pure and Apllied Mathematics, 2013 In this paper, we give sufficient conditions for a tuple of operators to be supercyclic.
B Yousefi, Gh.R. Moghimi
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