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 denoted as
The space of bounded sequences


 * $\ell^\infty$

can be seen written as:


 * $c_b$

Also see

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