Definition:Space of Bounded Sequences

Definition
The space of bounded sequences, denoted $\ell^\infty$ is defined as:


 * $\displaystyle \ell^\infty := \set{\sequence{z_n}_{n \in \N} \in \C^\N: \sup_{n \in \N} \size {z_n} < \infty}$

As such, $\ell^\infty$ is a subspace of $\C^\N$, the space of all complex sequences.

Also known as
The space of bounded sequences is also known as space of absolutely bounded sequences.

Also see

 * Definition:Supremum Norm
 * Definition:P-Sequence Space