Definition:Space of Bounded Sequences/Vector Space

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Definition

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

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

Let $+$ denote pointwise addition on the ring of sequences.

Let $\circ$ denote pointwise scalar multiplication on the ring of sequences.


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


Also see