My question is a mix of mathematical and historical, if you consider my question will be better answered in the mathematics community, please tell me.
I want to know the historical roots of Stone's representation theorem. Here is what I have found:
- In Stanford Encyclopedia of Philosophy, it says that one of the roots and applications of the duality is in the "algebra of projections (Functional analysis)"
- In "The theory of representations for Boolean algebras" M.H.Stone says:
The writer's interest in the subject, for example, arose in connection with the spectral theory of symmetric transformations in Hilbert space and certain related properties of abstract integrals.
I have tried to look in "Linear transformations in Hilbert Space and their application to analysis" by M.H.Stone, in the chapter IX "Symmetric transformations" but my knowledge in functional analysis is not very advanced and I'm not used to the old notation that is used in it.
What I'm trying to find is where do the boolean algebras and booleans rings appear in functional analysis.
Again, if you think could be better answered in mathematics section, i would be grateful if someone could tell how to redirect it.