Show that the map
A : (C[0,1],∥·∥∞) → R, Ax = x(0), ∀x ∈ C[0,1]
is a bounded linear operator.
I know one has to show the map is continuous but I'm not sure how to go about proving it in this case. Any help would and I will be very grateful.
There is another part to the question asking to find its operator norm.