How large is the space of almost convergent sequences?

Abstract

We consider the subspaces $c$, $\hat{c}$, $S$ of ${\ell }^{\infty }$, where $\hat{c}$ consists of almost convergent sequences, and $S$ consists of sequences whose arithmetic means of consecutive terms are convergent. We know that $c\subset \hat{c}\subset S$. We examine the largeness of $c$ in $\hat{c}$, $\hat{c}$ in $S$ and $S$ in ${\ell }^{\infty }$. We will do it from the viewpoints of porosity, algebrability and measure.

10 pages

References in corpus (1)

• Lineability in sequence and function spaces