Continuous projections onto ideal convergent sequences

Abstract

Let $\mathcal{I}\subseteq \mathcal{P}(\omega )$ be a meager ideal. Then there are no continuous projections from ${\ell }_{\infty }$ onto the set of bounded sequences which are $\mathcal{I}$-convergent to $0$. In particular, it follows that the set of bounded sequences statistically convergent to $0$ is not isomorphic to ${\ell }_{\infty }$.

5pp, no figures