# Normed linear space and inner product space

## Homework Statement

Not all normed linear spaces are inner product spaces. Give examples.

## Homework Equations

all equations and conditions constructing inner and normed linear spaces.

## The Attempt at a Solution

Well, I tried some of spaces like L space, but I didn't find any logical solutions. Frankly, I don't know from where to begin to prove this.

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morphism
Homework Helper
Try to flip through your book to find a property inner product spaces satisfy that is stated in terms of the norm generated by the inner product.

If you want another hint, post back.

I know all the sufficient properties for an inner product space, but how can I find a suitable example for this particular problem?

morphism
Homework Helper
Did you do what I suggested? What sufficient properties did you find?

ah, do you mean positive definiteness or parallelogram law?

morphism
Homework Helper
The latter is very useful!

yes,ok, but how should I write down the associated norm of a space which I don't know.

the only thing that I can write down is the parallelogram law itself which automatically yields the same thing in terms of inner product of its associated norm.

I am a bit confused...

morphism