Maximal spaceability in topological vector spaces

TL;DR

This paper introduces a new technique to establish the existence of large closed subspaces within certain topological vector sequence spaces, addressing previously unresolved questions in classical sequence spaces.

Contribution

It presents a novel method for proving maximal spaceability in topological vector spaces, expanding the understanding of spaceability in less-studied sequence spaces.

Findings

Established the existence of closed subspaces of maximal dimension in new classes of sequence spaces.

Resolved open questions regarding spaceability in classical sequence spaces.

Extended the theory of spaceability to broader classes of topological vector spaces.

Abstract

In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context of spaceability and settle some questions on classical sequence spaces that remained open.