Hello, I need some help with this exercise:

Let

T: $\displaystyle $L^1(R)$$ --->$\displaystyle $L^1(R)$$

$\displaystyle $\left( {T\phi } \right)\left( t \right) = \phi \left( {t + 1} \right)\$$

1) Prove T es la linear operator bounded and calculate it`s norm.

2) Calculate ker(T) and ran(T) this is the range I believe.

I started with linear operators 2 days ago.. I dont know all the theory yet, that`s why I`am asking for help.

Thanks!