What is the difference between l subscript infinity and l superscript infinity?

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The discussion clarifies the difference between l subscript infinity (ℓ₁) and l superscript infinity (ℓ∞). It is noted that ℓ∞ refers specifically to the space of bounded sequences, while ℓ₁ is often associated with summable sequences. The consensus is that ℓ∞ is the more commonly used notation for this space. Participants emphasize that both notations ultimately describe similar concepts in functional analysis. Understanding these distinctions is important for accurately discussing sequence spaces in mathematics.
bugatti79
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Folks,

Is there a difference between l subscript infinity and l superscript infinity. I believe the latter is the space if bounded sequences?

thanks
 
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I believe they both mean the same thing - the space of bounded infinite sequences. The more usual notation uses, I believe, superscript notation, like so
\ell^{\infty}
 

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