Editing Sequence (section)

====Sequence spaces====
{{main|Sequence space}}
A [[sequence space]] is a [[vector space]] whose elements are infinite sequences of [[real number|real]] or [[complex number|complex]] numbers. Equivalently, it is a [[function space]] whose elements are functions from the [[natural numbers]] to the [[Field (mathematics)|field]] ''K'', where ''K'' is either the field of real numbers or the field of complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in ''K'', and can be turned into a [[vector space]] under the operations of [[pointwise addition]] of functions and pointwise scalar multiplication. All sequence spaces are [[linear subspace]]s of this space. Sequence spaces are typically equipped with a [[norm (mathematics)|norm]], or at least the structure of a [[topological vector space]].

The most important sequences spaces in analysis are the ℓ<sup>''p''</sup> spaces, consisting of the ''p''-power summable sequences, with the ''p''-norm. These are special cases of [[Lp space|L<sup>''p''</sup> spaces]] for the [[counting measure]] on the set of natural numbers. Other important classes of sequences like convergent sequences or [[Sequence_space#c,_c0_and_c00|null sequence]]s form sequence spaces, respectively denoted ''c'' and ''c''<sub>0</sub>, with the sup norm. Any sequence space can also be equipped with the [[topology]] of [[pointwise convergence]], under which it becomes a special kind of [[Fréchet space]] called an [[FK-space]].