All Questions

What's the motivation for observables to be modeled by self-adjoint operators? I can't seem to find any place where this is laid out clearly. Maybe von Neumann's book is decent, but it's not ...

Let $T_+$ be the set of a positive trace-class operators over some separable Hilbert space and $A: T_+ \to \mathbb{R}\cup \{\infty\}$ some linear functional. In general, $A$ will not be continuous. ...

Let $H$ be a Hilbert space, $T_+(H)$ the set of positive self-adjoint trace-class operators on $H$, and $f : T_+(H) \to [0,m]$ a non-negative, bounded, convex functional. I don't necessarily know that ...