Spaces of sequences not converging to zero
Abstract
Let \(E\) be a Banach space (or a Banach lattice), let \(\tau\) be a vector topology on \(E\) and let \({\bf x}\) be a sequence (or a positive sequence) in \(E\) not converging to zero with respect to \(\tau\). We show how to construct infinite dimensional Banach spaces (or Banach lattices) consisting, up to the origin, of sequences in \(E\) not converging to zero with respect to \(\tau\) and containing a subsequence of \({\bf x}\). Plenty of applications to Banach space theory and to Banach lattice theory are provided.
Fields of Study & Subjects
Advanced Banach Space Theory
Approximation Theory and Sequence Spaces
Advanced Operator Algebra Research
Publication details
- Journal / source
- Annales Fennici Mathematici
- Volume
- 51
- Issue
- 1
- Pages
- 41–58
- Publication date
- 27 January 2026
- Language
- EN