# Banach space & Hilbert space

• May 24th 2011, 11:19 AM
manik
Banach space & Hilbert space
I need an example of a Banach space which is not a Hilbert space with proof.
• May 24th 2011, 11:27 AM
Ackbeet
Check out Kreyzsig's Introductory Functional Analysis with Applications, page 133. Your example is $l^{p},$ with $p\not=2.$
• May 24th 2011, 01:06 PM
Opalg
To prove that a Banach space is not a Hilbert space, show that its norm does not satisfy the parallelogram identity.