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One of the basic postulates in the mathematical formalism of quantum mechanics is that the probability of a measurement of an observable $A$ in the state $\psi \in \mathscr{H}$ to return a value in a ...

After the GNS representation for $C^{*}$-algebras is presented in Thirring's book Quantum mathematical physics, the author states the following theorem. The Spectral Theorem: For any given Hermitian (...

I suspect this is the obvious result of something in operator algebras, but that's far outside my field. Recall that a projection-valued measure is a map $E$ from a sigma-algebra $\mathcal{F}$ on ...

I was recently made aware (thanks to the answers on Why does Riesz's Representation Theorem apply in quantum mechanics?) that the $C^*$ algebra approach and the Hilbert space approach to quantum ...

$\DeclareMathOperator\CCR{CCR}\DeclareMathOperator\Im{Im}\DeclareMathOperator\PU{PU}$Let $V$ be a real vector space equipped with an antisymmetric bilinear form $\omega$. Recall that there is a $C^\...