przestrzeń Banacha

The notion of series can be easily extended to the case of a Banach space.

Measures that take values in Banach spaces have been studied extensively.

With respect to this norm bv becomes a Banach space as well.

Here is the Banach space of sequences converging to zero.

The same name is now used for the analogous construction for a Banach space.

Several concepts of a derivative may be defined on a Banach space.

This is a closed subspace of c, and so again a Banach space.

Finally, all of the above holds for integrals with values in a Banach space.

Compact operators on a Banach space are always completely continuous.

The direct sum with this norm is again a Banach space.