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An eventually-zero sequence is a real-valued sequence $(x_n)_{n=1}^\infty$ for which there exists an $N\in\mathbb{N}$ such that $x_n=0$ for each $n\geq N$. The space of eventually-zero sequences equipped with the sup-norm is usually denoted by $c_{00}$. I am working with the same underlying set of sequences, but in my case it is equipped with the $\ell^1$-norm. Is there any established notation for this space of sequences?

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    $\begingroup$ c_{00} or c_{00}(\mathbb{N}) is just a vector space it is not the convention that it is equipped with the sup-norm. $\endgroup$
    – Kevin Beanland
    Commented Apr 24, 2022 at 10:31
  • $\begingroup$ @KevinBeanland Thanks very much. That's a relief, because I like the notation $c_{00}$ for this space. $\endgroup$
    – HardyHulley
    Commented Apr 25, 2022 at 11:13

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