Definition:Space of Bounded Sequences

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Definition

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

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

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


Sources