Space of sequences converging to zero

The Banach space

c_{0}

consists of scalar sequences tending to zero with the supremum norm.

Table of contents
- Convergent sequence space Space of sequences converging to zero
  - Absorption of a finite-dimensional summand by c0 Convergent sequence space

Convergent sequence space

c

consists of convergent scalar sequences with the supremum norm.

Absorption of a finite-dimensional summand by c0

The map

(x_{n}) \mapsto (lim x_{n}, x_{1} - lim x_{n}, x_{2} - lim x_{n}, \dots)

proves

c ≅ c_{0}

, equivalently

c_{0} \oplus F ≅ c_{0}

.

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