Advances in Mathematics, ISSN 0001-8708, 04/2014, Volume 255, pp. 305 - 337

We first generalize the results of León-Saavedra and Müller (2006) [10] on hypercyclic subspaces to sequences of operators...

Hypercyclic subspaces | Hypercyclic operators | Weighted shifts | Primary | MATHEMATICS | UNIVERSAL | SPACES

Hypercyclic subspaces | Hypercyclic operators | Weighted shifts | Primary | MATHEMATICS | UNIVERSAL | SPACES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 2, pp. 1183 - 1195

.... By modifying a construction of Grivaux, we will show that the T-orbit of a hypercyclic vector can intersect certain closed vector subspaces of X in many strange ways...

Mixing | Set of visiting times | Subspace-hypercyclicity | Weak mixing | Hypercyclic operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS

Mixing | Set of visiting times | Subspace-hypercyclicity | Weak mixing | Hypercyclic operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS

Journal Article

Journal of Operator Theory, ISSN 0379-4024, 2015, Volume 73, Issue 2, pp. 385 - 405

We say that a sequence of operators (T-n) possesses hereditarily hypercyclic subspaces along a sequence (n(k...

Hypercyclic subspaces | Hypercyclic operators | MATHEMATICS | UNIVERSAL | hypercyclic subspaces | FRECHET SPACE | OPERATORS | VECTORS

Hypercyclic subspaces | Hypercyclic operators | MATHEMATICS | UNIVERSAL | hypercyclic subspaces | FRECHET SPACE | OPERATORS | VECTORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2015, Volume 432, Issue 1, pp. 10 - 37

We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences...

Hypercyclic subspaces | Common hypercyclic vectors | Frequently hypercyclic operators | MATHEMATICS | MATHEMATICS, APPLIED | UNIVERSAL | SPACES | FAMILIES | INVARIANT | MULTIPLES | VECTORS | OPERATORS

Hypercyclic subspaces | Common hypercyclic vectors | Frequently hypercyclic operators | MATHEMATICS | MATHEMATICS, APPLIED | UNIVERSAL | SPACES | FAMILIES | INVARIANT | MULTIPLES | VECTORS | OPERATORS

Journal Article

Constructive Approximation, ISSN 0176-4276, 10/2019, Volume 50, Issue 2, pp. 323 - 339

.... Such a criterion improves some already known special cases, and, in addition, it is also valid to provide dense vector subspaces as well as large closed ones consisting entirely, except for zero...

Lineability | 30E10 | 47B38 | Hypercyclic sequence of operators | 47A16 | Numerical Analysis | Analysis | Composition operator | Holomorphic function | 47B33 | Mathematics | Frequent hypercyclicity | MATHEMATICS | INVARIANT-MANIFOLDS | Mathematics - Complex Variables

Lineability | 30E10 | 47B38 | Hypercyclic sequence of operators | 47A16 | Numerical Analysis | Analysis | Composition operator | Holomorphic function | 47B33 | Mathematics | Frequent hypercyclicity | MATHEMATICS | INVARIANT-MANIFOLDS | Mathematics - Complex Variables

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2013, Volume 77, Issue 4, pp. 489 - 520

Known results about hypercyclic subspaces concern either Fréchet spaces with a continuous norm or the space ω...

Mathematics | Hypercyclic operators | Fréchet spaces | Primary 47A16 | Analysis | hypercyclic subspaces

Mathematics | Hypercyclic operators | Fréchet spaces | Primary 47A16 | Analysis | hypercyclic subspaces

Journal Article

Operators and Matrices, ISSN 1846-3886, 03/2018, Volume 12, Issue 1, pp. 205 - 214

Our aim in this paper is to obtain necessary and sufficient conditions for bilateral and unilateral weighted shift operators to be subspace-transitive...

Hypercyclic operators | Weighted shift operators | MATHEMATICS | weighted shift operators | OPERATORS

Hypercyclic operators | Weighted shift operators | MATHEMATICS | weighted shift operators | OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2013, Volume 408, Issue 1, pp. 209 - 212

A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a subspace M if Orb(T,x...

Hypercyclic operators | Subspace-hypercyclic operators | MATHEMATICS | MATHEMATICS, APPLIED

Hypercyclic operators | Subspace-hypercyclic operators | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 319, Issue 2, pp. 764 - 782

... } is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that it is possible to characterize Banach space operators that have a hypercyclic subspace, i.e...

Fréchet space | Hypercyclic | Hypercyclic subspace | Convolution operator | Hypercyclic spectrum | MATHEMATICS | hypercyclic | MATHEMATICS, APPLIED | hypercyclic subspace | UNIVERSAL | convolution operator | INVARIANT | Frechet space | hypercyclic spectrum

Fréchet space | Hypercyclic | Hypercyclic subspace | Convolution operator | Hypercyclic spectrum | MATHEMATICS | hypercyclic | MATHEMATICS, APPLIED | hypercyclic subspace | UNIVERSAL | convolution operator | INVARIANT | Frechet space | hypercyclic spectrum

Journal Article

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, 04/2019, Volume 113, Issue 2, pp. 487 - 505

We show that the non-zero multiples of the derivative operator and the non-zero multiples of non-trivial translation operators on the space of entire functions share a common hypercyclic subspace, i.e...

Common hypercyclic subspaces | Derivative operator | MATHEMATICS | Hypercyclic operators | 47A16 | Translation operators

Common hypercyclic subspaces | Derivative operator | MATHEMATICS | Hypercyclic operators | 47A16 | Translation operators

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 316, Issue 1, pp. 16 - 23

..., the countably infinite product of lines, has a common hypercyclic subspace.

Hypercyclic subspaces | Hypercyclic operators | Fréchet spaces | Frechet spaces | DENSE | MATHEMATICS, APPLIED | UNIVERSAL | MATHEMATICS | CHAOS | hypercyclic operators | hypercyclic subspaces | BANACH-SPACES | BACKWARD SHIFT | ORBITS | OPERATORS | VECTORS

Hypercyclic subspaces | Hypercyclic operators | Fréchet spaces | Frechet spaces | DENSE | MATHEMATICS, APPLIED | UNIVERSAL | MATHEMATICS | CHAOS | hypercyclic operators | hypercyclic subspaces | BANACH-SPACES | BACKWARD SHIFT | ORBITS | OPERATORS | VECTORS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2015, Volume 143, Issue 6, pp. 2469 - 2477

We study the existence and the non-existence of frequently hypercyclic subspaces of frequently hypercyclic operators living on Banach spaces...

Hypercyclic subspaces | Hypercyclicity | Weighted shifts | Frequent hypercyclicity | weighted shifts | MATHEMATICS | MATHEMATICS, APPLIED | hypercyclic subspaces | frequent hypercyclicity | OPERATORS

Hypercyclic subspaces | Hypercyclicity | Weighted shifts | Frequent hypercyclicity | weighted shifts | MATHEMATICS | MATHEMATICS, APPLIED | hypercyclic subspaces | frequent hypercyclicity | OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2020, Volume 487, Issue 1, p. 123960

We consider the subspace-hypercyclicity for abelian semigroups G of matrices on Kn (n≥1), K=RorC...

Dense orbit | Hypercyclic | Subspace-hypercyclic | Semigroup | Somewhere dense | Abelian | MATHEMATICS | TUPLES | MATHEMATICS, APPLIED | OPERATORS

Dense orbit | Hypercyclic | Subspace-hypercyclic | Semigroup | Somewhere dense | Abelian | MATHEMATICS | TUPLES | MATHEMATICS, APPLIED | OPERATORS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2006, Volume 134, Issue 7, pp. 1955 - 1961

In this note, we show that every infinite-dimensional separable Fréchet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors...

Mathematical manifolds | Topological theorems | Topological vector spaces | Separable spaces | Hilbert spaces | Scalars | Mathematical vectors | Topology | Banach space | Fréchet space | Backward shift | Hypercyclic sequence | Hypercyclic subspace | Hypercyclic operator | DENSE | MATHEMATICS, APPLIED | hypercyclic subspace | UNIVERSAL | INVARIANT-MANIFOLDS | hypercyclic sequence | OPERATOR ALGEBRA | MATHEMATICS | ELEMENTS | hypercyclic operator | BANACH-SPACES | backward shift | Frechet space | ORBITS | HILBERT-SPACE | SUPERCYCLIC SUBSPACES | VECTORS

Mathematical manifolds | Topological theorems | Topological vector spaces | Separable spaces | Hilbert spaces | Scalars | Mathematical vectors | Topology | Banach space | Fréchet space | Backward shift | Hypercyclic sequence | Hypercyclic subspace | Hypercyclic operator | DENSE | MATHEMATICS, APPLIED | hypercyclic subspace | UNIVERSAL | INVARIANT-MANIFOLDS | hypercyclic sequence | OPERATOR ALGEBRA | MATHEMATICS | ELEMENTS | hypercyclic operator | BANACH-SPACES | backward shift | Frechet space | ORBITS | HILBERT-SPACE | SUPERCYCLIC SUBSPACES | VECTORS

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2012, Volume 164, Issue 2, pp. 253 - 267

Let ( φ n ) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on ( φ n ) , we construct an H ( G )...

Composition operators | Dense-lineability | Universal functions | Hypercyclic vectors | Maximal cluster set | Spaceability | MATHEMATICS | LINEABILITY | INVARIANT-MANIFOLDS | OPERATORS

Composition operators | Dense-lineability | Universal functions | Hypercyclic vectors | Maximal cluster set | Spaceability | MATHEMATICS | LINEABILITY | INVARIANT-MANIFOLDS | OPERATORS

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2008, Volume 45, Issue 4, pp. 903 - 921

.... We consider the problem: given an operator T : X -> X, hypercylic or not, is the restriction T vertical bar y to some closed invariant subspace Y subset of X hypercyclic...

Extension | Hypercyclic | Restriction | Invariant subspace | NUCLEARLY ENTIRE-FUNCTIONS | MATHEMATICS | hypercyclic | MATHEMATICS, APPLIED | extension | invariant subspace | restriction | PDE-PRESERVING OPERATORS

Extension | Hypercyclic | Restriction | Invariant subspace | NUCLEARLY ENTIRE-FUNCTIONS | MATHEMATICS | hypercyclic | MATHEMATICS, APPLIED | extension | invariant subspace | restriction | PDE-PRESERVING OPERATORS

Journal Article

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, ISSN 1578-7303, 9/2011, Volume 105, Issue 2, pp. 415 - 421

If M is a closed subspace of a separable, infinite dimensional Hilbert space H with dim...

Hypercyclic extension | Infinite codimension | Invariant subspace | 47A15 | 47A16 | Theoretical, Mathematical and Computational Physics | Chaotic extension | Mathematics, general | 46A22 | Mathematics | Applications of Mathematics | MATHEMATICS | SPACES | HYPERCYCLICITY | Operators | Hilbert space | Criteria | Subspaces | Chaos theory | Linear operators

Hypercyclic extension | Infinite codimension | Invariant subspace | 47A15 | 47A16 | Theoretical, Mathematical and Computational Physics | Chaotic extension | Mathematics, general | 46A22 | Mathematics | Applications of Mathematics | MATHEMATICS | SPACES | HYPERCYCLICITY | Operators | Hilbert space | Criteria | Subspaces | Chaos theory | Linear operators

Journal Article

Monatshefte für Mathematik, ISSN 1436-5081, 2012, Volume 168, Issue 3-4, pp. 305 - 320

We study the existence of frequently hypercyclic subspaces for a given operator, that is, the existence of closed infinite-dimensional subspaces in which every non-zero vector is frequently hypercyclic...

Frequently hypercyclic operator | 47A16 | Mathematics, general | Mathematics | Frequently hypercyclic subspace | Left-multiplication operator | Frequently hypercyclic tensor product | MATHEMATICS | UNIVERSAL | SPACES | OPERATORS

Frequently hypercyclic operator | 47A16 | Mathematics, general | Mathematics | Frequently hypercyclic subspace | Left-multiplication operator | Frequently hypercyclic tensor product | MATHEMATICS | UNIVERSAL | SPACES | OPERATORS

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2018, Volume 274, Issue 10, pp. 2884 - 2905

We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on...

Composition operators | Hypercyclic subspaces | Hypercyclic algebras | Convolution operators | MATHEMATICS

Composition operators | Hypercyclic subspaces | Hypercyclic algebras | Convolution operators | MATHEMATICS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2001, Volume 353, Issue 1, pp. 247 - 267

...}. Our main result states that if T satisfies the Hypercyclicity Criterion and the essential spectrum intersects the closed unit disk, then there is an infinite-dimensional closed subspace consisting...

Integers | Mathematical theorems | Algebra | Spectral theory | Linear transformations | Separable spaces | Hilbert spaces | Mathematical vectors | Banach space | Backward shift | Differentiation operator | Hypercyclic vector | Bilateral shift | Essential spectrum | Composition operator | Multiplier | Translation operator | Essential minimum modulus | Hypercyclic operator

Integers | Mathematical theorems | Algebra | Spectral theory | Linear transformations | Separable spaces | Hilbert spaces | Mathematical vectors | Banach space | Backward shift | Differentiation operator | Hypercyclic vector | Bilateral shift | Essential spectrum | Composition operator | Multiplier | Translation operator | Essential minimum modulus | Hypercyclic operator

Journal Article

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