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arXiv · 1409.0995

Existence of common and upper frequently hypercyclic subspaces

Juan Bès·Quentin Menet
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Abstract

We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic subspaces and no frequently hypercyclic subspace. On the space of entire functions, each differentiation operator induced by a non-constant polynomial supports an upper frequently hypercyclic subspace, and the family of its non-zero scalar multiples has a common hypercyclic subspace. A question of Costakis and Sambarino on the existence of a common hypercyclic subspace for a certain uncountable family of weighted shift operators is also answered.

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Juan Bès, Quentin Menet. 2014-09-03. Existence of common and upper frequently hypercyclic subspaces. https://arxiv.org/abs/1409.0995

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