On the Existence of Infinite-Dimensional Closed Subspaces of Frequently Hypercyclic Vectors for $T_f$

Abstract

Motivated by recent studies on the notions of lineability and spaceability in the context of linear dynamics, we investigate the existence of infinite-dimensional closed subspaces of frequently hypercyclic vectors for frequently hypercyclic composition operators, known in the literature as Koopman operators and extensively used in many applications (like, for instance, the analysis of the dynamics of economic models formulated in terms of dynamical systems). All the results are obtained on $L^p$ spaces, $1 \leq p < \infty$, and in the dissipative setting with the extra hypothesis of bounded distortion. This allows us, as a consequence, to deduce analogous conclusions for fundamental mathematical objects: bilateral weighted backward shifts on $\ell^p$ spaces.