Hey there,

For a course in Functional Analysis we were asked to show that the norm of the n-th power of the Volterra operator is less than or equal to 1 over n!.

Show

Now I know how the operator norm is defined

and I've been throwing it at this problem for at least 3 hours, but I can't seem to crack it.

I've so far assumed that induction would be the path to choose but I'm starting to doubt that, yet I see no other method.

I hope someone is able to nudge me in the right direction.

Thanks,

Insensus