Infinity-norm and inner-product

Hey,

Could someone assist me in the following math-problem.

I want to show that the norm does not come from an inner product.

Hint: Show that the norm does not satisfy the paralellogram law, e.g., for

The paralellogram law states that if is a vector space with an inner product and associated norm , then:

Thanks in advance.

Infinity norm and inner-product

Hey,

Yes indeed I have tried myself. The following is what I have so far:

By definition I know that:

It is clear that:

Applying the definition in the beginning we have:

We conclude that the norm does not satisfy the parallelogram law. My question is : "How does this show that the infinity-norm does not come from an inner-product? Is is simply because the above shows that the infinity-norm does not fulfill the parallelogram law which is one of the requirements for a vectorspace with an inner-product and associated norm?"

Thanks.