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

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- May 24th 2011, 11:19 AMmanikBanach space & Hilbert space
I need an example of a Banach space which is not a Hilbert space with proof.

- May 24th 2011, 11:27 AMAckbeet
Check out Kreyzsig's

*Introductory Functional Analysis with Applications*, page 133. Your example is $\displaystyle l^{p},$ with $\displaystyle p\not=2.$ - May 24th 2011, 01:06 PMOpalg
To prove that a Banach space is not a Hilbert space, show that its norm does not satisfy the parallelogram identity.