Results 41 to 50 of about 92 (85)

Explicit Constructions of Dense Common Hypercyclic Subspaces

Publications of the Research Institute for Mathematical Sciences, 2007
We give an explicit construction of a dense infinite dimensional vector space of hypercyclic vectors for the weighted backward shift _T_λ (|λ| > 1). We also develop a technique to construct common hypercyclic vectors for countable families of these operators.
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Existence of common and upper frequently hypercyclic subspaces

Journal of Mathematical Analysis and Applications, 2015
We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic subspaces and no frequently hypercyclic subspace.
Juan Bès, Quentin Menet
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Hypercyclic subspaces for Fréchet space operators

Journal of Mathematical Analysis and Applications, 2006
Let \(X\) be a topological vector space. A linear continuous operator \(T:X\to X\) is said to be hypercyclic if there is a vector \(x\in X\) (called hypercyclic vector for \(T\)) such that its orbit under \(T\) is dense in \(X\). A hypercyclic subspace of \(T\) is a closed infinite-dimensional subspace \(H\subset X\) such that any nonzero vector of \(H\
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Hypercyclic orbits intersect subspaces in wild ways

Journal of Mathematical Analysis and Applications, 2017
Let us consider a linear operator $T\in L(X)$, with $X$ being an infinite-dimensional separable Banach space. \par It is known that the intersection of an orbit with a closed vector subspace $Y$ can be somewhere dense in $Y$ without being dense in $Y$, see [\textit{S. Grivaux}, Arch. Math. 81, No. 3, 291--299 (2003; Zbl 1056.47007); \textit{R.
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Disjoint subspace-hypercyclic operators on separable Banach spaces

Annals of Functional Analysis
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Renyu, Chen, Xiang, Zhou, Zehua
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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 \(X\).
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Hypercyclic subspaces for sequences of finite order differential operators

Journal of Mathematical Analysis and Applications
It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense $\mathfrak{c}$-dimensional subspace of entire functions, all of whose nonzero members are ...
L. Bernal-González, M.C. Calderón-Moreno, J. López-Salazar, J.A. Prado-Bassas   +3 more
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Some Results on Subspace Cesaro-Hypercyclic Operators

International Journal of Analysis and Applications
In this paper we characterize the notion of subspace Cesaro-hypercyclic. At the same time, we also provide a Subspace Cesaro-hypercyclic Criterion and offer an equivalent conditions of this criterion.
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A class of Toeplitz operators with hypercyclic subspaces

, 2013
5 ...
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SUFFICIENT CONDITIONS FOR SUBSPACE-HYPERCYCLICITY [PDF]

International Journal of Pure and Apllied Mathematics, 2015
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