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

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- Nov 8th 2011, 10:34 AMbugatti79Function Spaces
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 - Nov 8th 2011, 11:00 AMDevenoRe: Function Spaces
let . then ||f|| = 0, but f ≠ 0.

- Nov 8th 2011, 11:39 AMbugatti79Re: Function Spaces
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 - Nov 8th 2011, 12:11 PMTheEmptySetRe: Function Spaces
- Nov 8th 2011, 12:16 PMbugatti79Re: Function Spaces
- Nov 8th 2011, 12:21 PMTheEmptySetRe: Function Spaces
- Nov 8th 2011, 12:52 PMbugatti79Re: Function Spaces
- Nov 8th 2011, 12:57 PMTheEmptySetRe: Function Spaces