Let and be the -norm and the -norm on the space of continuous real valued functions on the closed interval : explicitly
For , define by
Caculate and .
So the thing is that I've been ill for over a week now and couldn't go to lectures resulting in me not having lecture notes and no notion of norms.
I am confused by the sequence of functions which I don't really know how to interpret (what is it geometrically?) or plug into , . Do I find the limit of the sequence or what do I do to compute and ?