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- W4286793357 abstract "Let $mathscr{F}=(F_n)$ be a sequence of nonempty finite subsets of $omega$ such that $lim_n |F_n|=infty$ and define the ideal $$mathcal{I}(mathscr{F}):=left{Asubseteq omega: |Acap F_n|/|F_n|to 0~mbox{as}~nto infty right}.$$ The case $F_n={1,ldots,n}$ corresponds to the classical case of density zero ideal. We show that $mathcal{I}(mathscr{F})$ is an analytic P-ideal but not $F_{sigma}$. As a consequence, we show that the set of real bounded sequences which are $mathcal{I}(mathscr{F})$-convergent to $0$ is not complemented in $ell_infty$." @default.
- W4286793357 created "2022-07-24" @default.
- W4286793357 creator A5027292956 @default.
- W4286793357 date "2020-05-25" @default.
- W4286793357 modified "2023-10-17" @default.
- W4286793357 title "A generalization of the density zero ideal" @default.
- W4286793357 doi "https://doi.org/10.48550/arxiv.2005.12355" @default.
- W4286793357 hasPublicationYear "2020" @default.
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