What does the $\ell_\infty$ space stand for?
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A web search for "l infinity" led to a Wikipedia page for $L^p$ spaces, which includes a section on $\ell^p$ spaces, which is an alternative notation for $\ell_p$ spaces. As stated there, $\ell^\infty$ is the space of bounded sequences. So $\ell_\infty$ is the same thing with different notation.