Results 31 to 40 of about 559 (116)
Hypercyclic operators with an in¯nite dimensional closed subspace of periodic points
Revista Matemática Complutense, 2003 Let \(X\) be an infinite-dimensional real or complex separable Banach space \(X\). If \(T\) is a bounded operator on \(X\), a vector \(x\) of \(X\) is said to be hypercyclic for \(T\) if the orbit of \(x\) under \(T\), that is, the set \(\{T^{n}x: n \geq 0 \}\), is dense in \(X\).
Sophie Grivaux
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Strongly mixing convolution operators on Fr\'echet spaces of holomorphic functions [PDF]
, 2014 A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on $\mathbb{C}^n$ are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of ...
Muro, Santiago +2 more
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Hypercyclic subspaces in omega
Journal of Mathematical Analysis and Applications, 2006 A continuous linear operator \(T\) acting on a Fréchet space \(X\) is called hypercyclic if there exists a vector \(x\in X\) whose orbit Orb\((T,x)=\{x, T(x), T^2(x), \ldots\}\) is dense in \(X\). Such a vector \(x\) is called a hypercyclic vector for \(T\). A hypercyclic manifold for \(T\) is a dense, invariant subspace of \(X\) consisting entirely --
Bès, Juan, Conejero, José A.
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Abstract and Applied Analysis, Volume 2018, Issue 1, 2018., 2018 The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
G. M. N’Guérékata +2 more
wiley +1 more source
S‐Mixing Tuple of Operators on Banach Spaces
Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016 We consider the question: what is the appropriate formulation of Godefroy‐Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, S‐mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be S‐mixing.
Wei Wang +3 more
wiley +1 more source
Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces
Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015 We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.
Zoryana Mozhyrovska +2 more
wiley +1 more source
Subspace-diskcyclic sequences of linear operators [PDF]
Sahand Communications in Mathematical Analysis, 2017 A sequence ${T_n}_{n=1}^{infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}
Mohammad Reza Azimi
doaj
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
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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Dynamics of non-convolution operators and holomorphy types [PDF]
, 2018 In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces.
Muro, Luis Santiago Miguel +2 more
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