Results 31 to 40 of about 893 (111)

J-class weighted shifts on the space of bounded sequences of complex numbers

, 2008
We provide a characterization of $J$-class and $J^{mix}$-class unilateral weighted shifts on $l^{\infty}(\mathbb{N})$ in terms of their weight sequences. In contrast to the previously mentioned result we show that a bilateral weighted shift on $l^{\infty}
Costakis, George, Manoussos, Antonios
core   +1 more source

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, María del Pilar Romero-de la Rosa, Manuel Maestre   +2 more
wiley   +1 more source

Banach spaces of hypercyclic vectors.

Michigan Mathematical Journal, 1996
Dirección General de Investigación Científica y ...
openaire   +4 more sources

Common Hypercyclic Vectors for High-Dimensional Families of Operators [PDF]

International Mathematics Research Notices, 2015
Let $(T\_\lambda)\_{\lambda\in\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of $\mathbb R^d$. We give sufficient conditions on the family to yield the existence of a vector $x\in X$ such that, for any $\lambda\in\Lambda$, the set $\big\{T\_\lambda^n x;\ n\geq 1\big\}$ is dense in $X$.
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   +1 more source

Plank theorems and their applications: A survey

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley   +1 more source

Common hypercyclic vectors and dimension of the parameter set

Indiana University Mathematics Journal, 2022
We investigate the existence of a common hypercyclic vector for a family $(T_ )_{ \in }$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of $ $ and the regularity of each map $ \in \mapsto T_ ^n x$, $x\in X$, $n\in\mathbb N$.
Bayart, Frédéric, Costa, Fernando, Menet, Quentin   +2 more
openaire   +4 more sources

Interactions between universal composition operators and complex dynamics

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract This paper is concerned with universality properties of composition operators Cf$C_f$, where the symbol f$f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of Cf$C_f$ when f$f$ is restricted to (subsets of) Baker and wandering domains.
Vasiliki Evdoridou, Clifford Gilmore, Myrto Manolaki   +2 more
wiley   +1 more source

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., Alfredo Peris, Ajda Fošner   +2 more
wiley   +1 more source

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   +4 more sources