Sequence space

Vector space of infinite sequences

In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field ⁠ K {\displaystyle \mathbb {K} } ⁠ of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in ⁠ K {\displaystyle \mathbb {K} } ⁠, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.

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