# Tagged Questions

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vote

**1**answer

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### Folium in GNS construction and von Neumann algebras

The GNS construction allows one to represent a $C^*$-algebra as the algebra of bounded operators on a Hilbert space when a state is fixed, this state being represented as a vector on the Hilbert ...

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**1**answer

268 views

### Topology of the “normal spectrum” of a commutative von Neumann algebra

Kadison and Ringrose define normal states $\omega$ of a von Neumann algebra $A$ as such that $\omega(H_\alpha)\to \omega(H)$ for each monotone increasing net of operators $H_\alpha$ with least upper ...

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**2**answers

284 views

### ED compact $K$ such that $C(K)$ is not a dual Banach space

Almost every mathematician working in von Neumann algebras says that there are certainly extremely disconnected compact spaces $K$ such that $C(K)$ is not a dual space (they are not hyperstonean). ...

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503 views

### Which complete Boolean algebras arise as the algebras of projections of commutative von Neumann algebras?

Projections in an arbitrary commutative von Neumann algebra form a complete Boolean algebra.
Moreover, a morphism of commutative von Neumann algebras induces
a continuous morphism of the corresponding ...

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**4**answers

2k views

### Reference for the Gelfand-Neumark theorem for commutative von Neumann algebras

The Gelfand-Neumark theorem for commutative von Neumann algebras states that the following three categories are equivalent:
(1) The opposite category of the category of commutative von Neumann ...