# Thread: Banach space & Hilbert space

1. ## Banach space & Hilbert space

I need an example of a Banach space which is not a Hilbert space with proof.

2. Check out Kreyzsig's Introductory Functional Analysis with Applications, page 133. Your example is $l^{p},$ with $p\not=2.$

3. To prove that a Banach space is not a Hilbert space, show that its norm does not satisfy the parallelogram identity.