Hi,I want to prove that the sets
B_{n} ={g : 0 ≤ g ≤n} are weakly compact in σ(L^{∞},L^{1}).
Thank you for your help
The unit ball of is weak*-compact (that is, compact in the -topology). So all you have to do to prove that is weak*-compact is to show that it is weak*-closed in the unit ball of . The result for general then follows by taking scalar multiples.