Von Neumann Algebras

By Vaughan F. R. Jones. 2009

251 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/38acbe3c8ec01c9c0fb2ed6e7aa91bdfdc103da0

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Citations in the corpus

Character rigidity for special linear groups (2013, unknown): “For more details on all this and definitions of all terms please consult [10].”
Symmetries in Quantum Field Theory and Quantum Gravity (2018, background): “[53]), so we can view the split property as saying that, although the Hilbert space does not factorize based on spatial regions (in fact the algebra A[R] is expected to be type III for any nontrivial R), by gradually “thinning out” the algebra between R and R′ we can find a tensor factor whose opera”
Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces (2012, methodology): “Following [16] we therefore obtain a measurable field of Hilbert spaces, [15, 62].”
The Geometry and Topology of Coxeter Groups (2025, background): “As in [100] there are two von Neumann algebras associated with this situation.”
TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “The theory of operator algebras is in general quite intricate [82], but in finite-dimensional Hilbert spaces it is manageable.”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “The source from which I found this extraction the easiest is [89], whose presentation I have followed fairly closely.”
Operator Integrals, Spectral Shift, and Spectral Flow (2007, unknown): “(ii) This follows from the fact that two representations of a von Neumann algebra can be obtained from each other by ampliation, reduction, and spatial isomorphism [17], since for each of these isomorphisms the claim is evident.”
Notes on Some Entanglement Properties of Quantum Field Theory (2018, background): “For general mathematical background on von Neumann algebras, a convenient reference is the lecture notes of Jones [28].”
Model theory of operator algebras I: stability (2009, background): “The completion of M with respect to this metric is isomorphic to a Hilbert space (see, for example, [6] or [21]).”