Definition:Space of Bounded Sequences/Normed Vector Space

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Definition

Let $\mathbb F \in \set {\R, \C}$.

Let $\map {\ell^\infty} {\mathbb F}$ be the vector space of bounded sequences on $\mathbb F$.

Let $\norm \cdot_\infty$ be the supremum norm on the space of bounded sequences.


We say that $\struct {\map {\ell^\infty} {\mathbb F}, \norm \cdot_\infty}$ is the normed vector space of bounded sequences on $\mathbb F$.


Also see