Complemented hypercyclic subspaces

• Autores: Henrik Petersson
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 2, 2007, págs. 541-553
• Idioma: inglés
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• Resumen

  • A sequence T=(Tn) of continuous linear operators Tn acting on a space X, is said to be hypercyclic if there is a vector x, called hypercyclic for T, such that (Tnx) forms a dense set. A hypercyclic subspace for T is an infinite dimensional closed subspace of X formed by, except for zero, hypercyclic vectors (for T). We establish a criterion for a sequence T of operators, acting on a separable Frechet space with a continuous norm, to have a complemented hypercyclic subspace. Our result complements previous results by several authors.