Hypercyclic operators on countably dimensional spaces

A. Schenke, S. Shkarin

Research output: Contribution to journalArticlepeer-review

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Abstract

According to Grivaux, the group GL(X) of invertible linear operators on a separable infinite dimensional Banach space X acts transitively on the set s (X) of countable dense linearly independent subsets of X. As a consequence, each A? s (X) is an orbit of a hypercyclic operator on X. 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 X, GL(X) acts transitively on s (X) if and only if X possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator.
Original languageEnglish
Pages (from-to)209-217
Number of pages9
JournalJournal of Mathematical Analysis and its Applications
Volume401
Issue number1
DOIs
Publication statusPublished - 01 May 2013

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