Questions in linear recurrence: From the $T\oplus T$-problem to lineability

Autor:	Grivaux, Sophie, López-Martínez, Antoni, Peris, Alfred
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis Mathematics - Dynamical Systems 47A16 37B20 37B02
Druh dokumentu:	Working Paper
Popis:	We study, for a continuous linear operator $T$ on an F-space $X$, when the direct sum operator $T\oplus T$ is recurrent on $X\oplus X$. In particular: we establish the analogous notion, for recurrence, to that of (topological) weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and we construct a recurrent but not quasi-rigid operator on each separable infinite-dimensional Banach space, solving the $T\oplus T$-recurrence problem in the negative way. The quasi-rigidity notion is closely related to the dense lineability of the set of recurrent vectors, and using similar conditions we study the lineability and dense lineability properties for the set of $\mathcal{F}$-recurrent vectors, under very weak assumptions on the Furstenberg family $\mathcal{F}$. Comment: 37 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.03652 Zobrazit plný text záznamu View this record from Arxiv