Convergent sequence space

c

consists of convergent scalar sequences with the supremum norm.

Table of contents
- Absorption of a finite-dimensional summand by c0 Convergent sequence space

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}

.

 Ancestors (6)

 Incoming links (4)

Banach limit
Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 6 / 2 / Solution
Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 8 / 1 / Solution
Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 6 / 5 / b / Solution

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