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Hypercyclic operators on countably dimensional spaces
- Source :
-
Journal of Mathematical Analysis & Applications . May2013, Vol. 401 Issue 1, p209-217. 9p. - Publication Year :
- 2013
-
Abstract
- Abstract: According to Grivaux, the group of invertible linear operators on a separable infinite dimensional Banach space acts transitively on the set of countable dense linearly independent subsets of . As a consequence, each is an orbit of a hypercyclic operator on . Furthermore, every countably dimensional normed space supports a hypercyclic operator. Recently Albanese extended this result to Fréchet spaces supporting a continuous norm. We show that for a separable infinite dimensional Fréchet space , acts transitively on if and only if possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 401
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 85178352
- Full Text :
- https://doi.org/10.1016/j.jmaa.2012.11.013