Results 21 to 30 of about 184 (111)
Studia Mathematica, 2002 Let \(T: H\to H\) be a continuous linear operator on a separable Hilbert space. The orbit of a subset \(C\) of \(H\) under \(T\) is the union of the sets \(C,T(C),T^2(C),\dots\)\ . For a natural number \(n\), an operator is called \(n\)-supercyclic if there is an \(n\)-dimensional subspace of \(H\) whose orbit under \(T\) is dense in \(H\).
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An Extension of Hypercyclicity for N‐Linear Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Grosse‐Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N‐linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N‐linear ...
Juan Bès +2 more
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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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Powers of Convex‐Cyclic Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex‐cyclic operators. We provide an example of a convex‐cyclic operator T such that the power Tn fails to be convex cyclic.
Fernando León-Saavedra +2 more
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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
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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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n-supercyclic and strongly n-supercyclic operators in finite dimensions [PDF]
Studia Mathematica, 2014 We prove that on $\mathbb{R}^n$, there is no $N$-supercyclic operator with $1\leq N< \lfloor \frac{n+1}{2}\rfloor$ i.e. if $\mathbb{R}^n$ has an $N$ dimensional subspace whose orbit under $T$ is dense in $\mathbb{R}^n$, then $N$ is greater than $\lfloor\frac{n+1}{2}\rfloor$. Moreover, this value is optimal.
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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
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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
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Cyclicity of the adjoint of weighted composition operators on the Hilbert space of analytic functions [PDF]
, 2011 summary:In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic ...
Hedayatian, Karim +2 more
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