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Math Help - Banach space & Hilbert space

  1. #1
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    Banach space & Hilbert space

    I need an example of a Banach space which is not a Hilbert space with proof.
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  2. #2
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    Check out Kreyzsig's Introductory Functional Analysis with Applications, page 133. Your example is l^{p}, with p\not=2.
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  3. #3
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    To prove that a Banach space is not a Hilbert space, show that its norm does not satisfy the parallelogram identity.
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