Can a Function Go to Zero on NORM 1 but Not on NORM 2 on C[a,b]?

[lom]

how to think about a function on C[a,b] which goes to zero on NORM 1
but NOT on NORM2

i got a solution but it very complicated

i don't know how to predict how integrral will workout

i need a function and intervals

 

[LCKurtz]

You might tell us what norms are "Norm 1" and "Norm 2" instead of having us guess.

 

[lom]

norm one is like iner product integral deffinition
but norm

norm 2 is the squere of the absolute value in that integral