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arXiv · 1811.08206

Continuous projections onto ideal convergent sequences

Paolo Leonetti
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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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Paolo Leonetti. 2018-11-20. Continuous projections onto ideal convergent sequences. https://doi.org/10.1007/s00025-018-0876-8

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