2.1 Banach Spaces

Question 1

What is a Banach space?

Answer 1

A Banach space is a complete normed linear space, or a normed linear space X in which every Cauchy sequence converges to a point x belonging to X.

Question 2

What are some examples of Banach spaces?

Answer 2

1. The normed linear space ℝ with the norm: ||x|| = |x|
2. The normed linear space ℂ with the norm: ||z|| = |z|
3. The normed linear space l^p with norm ||x|| = (∑ |xᵢ|^p)^(1/p)