English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study, for a continuous linear operator $T$ on an F-space $X$, when thedirect sum operator $T\oplus T$ is recurrent on $X\oplus X$. In particular: weestablish the analogous notion, for recurrence, to that of (topological)weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and weconstruct a recurrent but not quasi-rigid operator on each separableinfinite-dimensional Banach space, solving the $T\oplus T$-recurrence problemin the negative way. The quasi-rigidity notion is closely related to the denselineability of the set of recurrent vectors, and using similar conditions westudy the lineability and dense lineability properties for the set of$\mathcal{F}$-recurrent vectors, under very weak assumptions on the Furstenbergfamily $\mathcal{F}$.

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