The Wikipedia article on predual states without proof:
For example, the predual of the space of bounded operators is the space of trace class operators.
How to prove this? Alternatively, could you suggest me a reference (with the exact section or page number) where I can look this up?
P.S: I haven't taken a formal class in functional analysis but I need to understand this in order to understand a certain concept in quantum information theory. So something at the beginners level would be helpful.
Let $B (H) $ be the algebra of bounded linear operators on $H $ and $L^1 (H) $ the trace-class operators. Define $\gamma:B (H)\to L^1 (H)^*$ by $$\gamma (T)(S)=\operatorname {Tr}(TS). $$ It is not hard to check that $\gamma $ is linear and isometric, so it gives an embedding of $B (H) $ into the dual of $L^1 (H) $. And, with some work, one can check that $\gamma $ is also surjective.