As an example of an inner product space that is not a Hilbert space, consider the inear space C[a, b] (Example 1.2) with inner product of f, g € C[a, b] defined to be (f. g) = f*f(x)g(x) dx. f a sequence of functions from C[a, b], {f} converges with respect to the norm lefined by this inner product, they will only converge “in the mean!" Since mean convergence does not necessarily imply uniform convergence it is seen that this paces does not have to be complete and the counterexample Example 4.4) shows hat this is actually so. Request explain which is this norm?

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A: Solution :-

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A: In order to solve this problem you need to know the following notions:

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Q: sup norm

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