Folks,
a) Does the function space defined by define a norm on C[0,1]
b)If it does, prove all the axioms for a norm hold. If not, demonstrate by an example some axiom which fails
How do I start a)....I have no idea....?
THanks
What I have in my notes is that a norm on a vector space V is a function || ||:V to R satisfying x and y in V and for all scalars alpha. One of the axioms states that ||x||=0 IFF x vector = zero vector.
Hence the above function does not define a norm...not sure how to rigorously prove it though...?
THanks