Sequence spaces Sequence

a sequence space vector space elements infinite sequences of real or complex numbers. equivalently, function space elements functions natural numbers field k, k either field of real numbers or field of complex numbers. set of such functions naturally identified set of possible infinite sequences elements in k, , can turned vector space under operations of pointwise addition of functions , pointwise scalar multiplication. sequence spaces linear subspaces of space. sequence spaces typically equipped norm, or @ least structure of topological vector space.

the important sequences spaces in analysis ℓ spaces, consisting of p-power summable sequences, p-norm. these special cases of l spaces counting measure on set of natural numbers. other important classes of sequences convergent sequences or null sequences form sequence spaces, respectively denoted c , c0, sup norm. sequence space can equipped topology of pointwise convergence, under becomes special kind of fréchet space called fk-space.