# Thread: Inner Product space not induced by L1 norm

1. ## Inner Product space not induced by L1 norm

I am trying to find a counterexample to the parallelogram law to show that the L1 norm is not induced by an inner product in [0,1]. I have found one where I can let f(x) = 1 for x in [0,1] and
g(x) = 1 for x in [1,2]
However, I want one just where the integral has limits 1 and 0 (i.e. just [0,1]).

Thanks.

2. Ok, I have managed to find that f(t) = t and g(t) = 1 - t do not satisfy parallelogram law for the norm of continuous functions in [0,1] to show that this norm is not induced by an inner product.....but after calculating, the parallelogram law is satisfied for these f,g for the L1 norm when I do not want it to be