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What have you tried so far? Can you think of results that might help here (Cauchy–Schwarz inequality perhaps, for a suitable choice of g)?consider C[0,2], the set of continous functions from [0,2] to C.
The inner product is <f,g> = the integral of f(t)g(t)* from 0 to 2.
show that:
sqrt(2)||f|| is greater than or equal to the magnitude of the integral of f from 0 to 2, where ||.|| is the norm of f.
I've tried writing what each side is. I don't see how schwarz inequality is relevant. I'm interested in f, not g.What have you tried so far? Can you think of results that might help here (Cauchy–Schwarz inequality perhaps, for a suitable choice of g)?