Hypercyclic subspaces and weighted shifts

By Quentin Menet. 2012

58 citations recorded by the source corpus.

Abstract We first generalize the results of Leon-Saavedra and Muller (2006) [10] on hypercyclic subspaces to sequences of operators on Frechet spaces with a continuous norm. Then we study the particular case of iterates of an operator T and show a simple criterion for having no hypercyclic subspace. Finally we deduce from this criterion a characterization of weighted shifts with hypercyclic subspaces on the spaces l p or c 0 , on the space of entire functions and on certain Kothe sequence spaces. We also prove that if P is a non-constant polynomial and D is the differentiation operator on the space of entire functions then P ( D ) possesses a hypercyclic subspace.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef1c0b81c3ca35737a5a91340e65821c115d8f24

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In Algebra and Number Theory

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda

In Applied Mathematics

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda

In Mathematical Physics

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda

Citations in the corpus

• Linear subsets of nonlinear sets in topological vector spaces (2013, methodology): “In 2011, Menet [220] has proved the assertion if X is a Fréchet space admitting a continuous norm, and the same author [221] has recently shown the same result for Fréchet spaces admitting a continuous seminorm p with codim(ker p) = ∞.”