How large is the space of almost convergent sequences?
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914410311712768 |
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| author | Nowakowski, Piotr |
| author_facet | Nowakowski, Piotr |
| contents | We consider the subspaces $c$, $\widehat{c}$, $S$ of $\ell^\infty$, where $\widehat{c}$ consists of almost convergent sequences, and $S$ consists of sequences whose arithmetic means of consecutive terms are convergent. We know that $c\subset \widehat{c} \subset S$. We examine the largeness of $c$ in $\widehat{c}$, $\widehat{c}$ in $S$ and $S$ in $\ell^\infty$. We will do it from the viewpoints of porosity, algebrability and measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05904 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | How large is the space of almost convergent sequences? Nowakowski, Piotr Functional Analysis 08B20, 40A05, 28A35 We consider the subspaces $c$, $\widehat{c}$, $S$ of $\ell^\infty$, where $\widehat{c}$ consists of almost convergent sequences, and $S$ consists of sequences whose arithmetic means of consecutive terms are convergent. We know that $c\subset \widehat{c} \subset S$. We examine the largeness of $c$ in $\widehat{c}$, $\widehat{c}$ in $S$ and $S$ in $\ell^\infty$. We will do it from the viewpoints of porosity, algebrability and measure. |
| title | How large is the space of almost convergent sequences? |
| topic | Functional Analysis 08B20, 40A05, 28A35 |
| url | https://arxiv.org/abs/2208.05904 |