M manik Feb 2010 10 0 Bangladesh May 24, 2011 #1 I need an example of a Banach space which is not a Hilbert space with proof.

A Ackbeet Jun 2010 6,318 2,433 CT, USA May 24, 2011 #2 Check out Kreyzsig's Introductory Functional Analysis with Applications, page 133. Your example is \(\displaystyle l^{p},\) with \(\displaystyle p\not=2.\)

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

Opalg Aug 2007 4,041 2,789 Leeds, UK May 24, 2011 #3 To prove that a Banach space is not a Hilbert space, show that its norm does not satisfy the parallelogram identity. Reactions: Ackbeet

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