1. May 14, 2015

### Ssnow

I want to ask if it is wrong to interpret the von Neumann density in a '' functional sense'' as a szego projector Hilbert spaces?
thks

2. May 14, 2015

### bhobba

I don't know what they are, but since density matrices are, by definition, defined on Hilbert spaces, that would seem rather difficult unless you change the concept in some way.

In case you haven't seen it here is the exact definition, which is part of the Born Rule

There exists a positive operator of unit trace, P, called the state of the system, such that if O is an observable, E(O), the expected outcome of the observation, is E(O) = Trace (PO).

P is also called the density matrix, but its not my preferred term.

As to why its true check out post 137:

Thanks
Bill

3. May 15, 2015

### Ssnow

Szego projectors are orthogonal projectors from the Hardy space H(X) to L^2 (an equivariant component), It seems that all POMV requirements are satisfied but not the condition on the trace that bust be 1 ... now my question is if I can interpret these Szego projectors (that in general are not matrices but more similar to oscillatory integrals (his kernel)) as a family of POVM that respect the Born rule.