c_0 Space

The space is the Banach space of real or complex sequences tending to zero, with the supremum norm:

The scalar field is specified by the context. More generally, consists of sequences in a Banach space whose norms tend to zero, with the same supremum convention. In particular, is the space of square-summable-vector-valued sequences tending to zero. These spaces appear in the Lipschitz isomorphism problem.