Hypercyclic subspaces for Fréchet space operators |
| |
Authors: | Henrik Petersson |
| |
Institution: | Chalmers/Göteborg University, School of Mathematical Sciences, SE-412 96 Göteborg, Sweden |
| |
Abstract: | A continuous linear operator is hypercyclic if there is an x∈X such that the orbit {Tnx} 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., an infinite dimensional closed subspace H⊆X of, except for zero, hypercyclic vectors. The following is known to hold: A Banach space operator T has a hypercyclic subspace if there is a sequence (ni) and an infinite dimensional closed subspace E⊆X such that T is hereditarily hypercyclic for (ni) and Tni→0 pointwise on E. In this note we extend this result to the setting of Fréchet spaces that admit a continuous norm, and study some applications for important function spaces. As an application we also prove that any infinite dimensional separable Fréchet space with a continuous norm admits an operator with a hypercyclic subspace. |
| |
Keywords: | Hypercyclic Hypercyclic subspace Hypercyclic spectrum Fré chet space Convolution operator |
本文献已被 ScienceDirect 等数据库收录! |
|