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Continuous projections onto ideal convergent sequences
Published 20 Nov 2018 in math.FA and math.GN | (1811.08206v1)
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 $\ell_\infty$.
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