I have started studing linear functionals and have looked at shift operators and multiplication operatotrs briefly. However, I have come across a problem as to how to answer the following questions:

1. Let the linear functional A: C[-1,1]-> R be defined by

A(f) = integral [t^2. f(t)] dt for all f in C[0,1] [limits of integral are +1,-1]

Find the operator norm of A.

2. Let the linear functional A: C[-1,1]-> R be defined by

A(f) = integral [t f(t)] dt for all f in C[0,1] [limits of integral are +1,-1]

Find the operator norm of A.

If someone could show a method of as how to do Qu1, I think I could apply that idea to do Qu2. Sorry for the trouble but would be very grateful if you could help

Thanks!