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What does the $\ell_\infty$ space stand for?

Thank you.

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    @tomcuchta: That is not generally true. E.g., consider a nonzero constant sequence. But it is true for elements of $\bigcup\limits_{p\in [1,\infty)}\ell_p$.2011-11-09

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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.