Sequence space

Summary

A sequence space is a vector space whose elements are infinite sequences of real or complex numbers, with termwise addition and scalar multiplication. Standard examples are the spaces ℓ^p, the space of convergent sequences and the space of null sequences. Sequence spaces give the simplest examples of infinite-dimensional normed and topological vector spaces. In summability theory, the sequences summable by a matrix method form a sequence space, and functional analysis is used to study it.