How to figure whether it is a compact operator How to figure whether it is a compact operator:
$$T:C[0,1]\rightarrow C[0,1] $$ $C[0,1]$:the space of all continous function on [0,1] with supremum norm
$$(Tx)(t)=\int^t_0 x(s)ds, \ \ \forall t\in[0,1]$$
Could you please help with this question.

Sketch 


*

*You are to prove that the image of the unit ball $B \subset C[0,1]$ is precompact in $C[0,1]$. 

*Because of the fundamental theorem of calculus, you have a nice description of $T(B)$.

*Use said description to show that $T(B)$ is equicontinuous. 

*Apply Arzelà–Ascoli.
