Nacib G. Albuquerque | Searcharxiv

arXiv2026

On hypercyclic spaces and (common) $\mathscr{U}$-frequently hypercyclic spaces

Let $B$ be an unilateral weighted backward shift on $\ell_p$, $1 \leq p < \infty$, that admits a $\mathscr{U}$-frequently hypercyclic subspace. We prove that $B$ admits such a subspace free of frequently hypercyclic vectors. The proof technique we develop also allows us to prove that $B$ admits a hypercyclic subspace free of $\mathscr{U}$-frequently hypercyclic vectors, and to solve a question posed by Bès and Menet in 2015 on the existence of common $\mathscr{U}$-frequently hypercyclic subspaces.

math.FA↗

arXiv2026

Geometric spaceability in sequence classes and operator ideals

This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous classical sequence spaces while preserving their fundamental behavior. Utilizing this framework, we establish general $(α, \mathfrak{c})$-spaceability results for complements of unions of (quasi-)Banach sequence spaces. These results extend the existing literature by addressing the geometrically more demanding case where $α> 1$ and by encompassing the non-locally convex (quasi-)Banach setting. Furthermore, we provide criteria for the pointwise $\mathfrak{c}$-spaceability of differences between general operator ideals with values in standard sequence spaces. Our results recover and improve several known findings in the context of vector-valued sequences.

math.FA↗