Topological and algebraic genericity and spaceability for an extended chain of sequence spaces

TL;DR

This paper investigates the topological and algebraic genericity and spaceability properties within an extended chain of sequence spaces, including the classical ll^p spaces, highlighting their structural richness.

Contribution

It introduces a unified framework for analyzing genericity and spaceability across a broad class of sequence spaces, extending previous results to an extended chain including ll^p spaces.

Findings

Establishes genericity and spaceability results for pairs of sequence spaces.

Provides a comprehensive analysis applicable to a wide class of sequence spaces.

Extends known properties from classical ll^p spaces to more general chain structures.

Abstract

We examine topological and algebraic genericity and spaceability for any pair $(X,Y)$, $X\subset Y$, $X\neq Y$ belonging to an extended chain of sequence spaces which contains the $\ell^p$ spaces, $0<p\leq \infty$.