Quasi-States on C ∗ -Algebras

Aarnes, Johan F.

doi:10.2307/1995417

Cited by 25 publications

(37 citation statements)

References 4 publications

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“…There is a beautiful and detailed paper by Maeda (Maeda, 1990) on the generalizations of Gleason's theorem. Maeda is drawing on results by Aarnes (1969Aarnes ( , 1970, Gunson (1972), Christensen (1982Christensen ( , 1985, Yeadon (1983Yeadon ( , 1984 and Saito (1985). The proofs given in Maeda's paper are by no means trivial.…”

Section: Von Neumann Algebras Without Type I 2 Summandmentioning

confidence: 98%

Kochen–Specker Theorem for von Neumann Algebras

Döring

2005

Int J Theor Phys

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The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the nonexistence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type I n factor as algebra of observables, including I ∞ . Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von Neumann algebra R without summands of types I 1 and I 2 , using a known result on two-valued measures on the projection lattice P(R). Some connections with presheaf formulations as proposed by Isham and Butterfield are made.

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Section: Von Neumann Algebras Without Type I 2 Summandmentioning

confidence: 98%

Kochen–Specker Theorem for von Neumann Algebras

Döring

2005

Int J Theor Phys

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“…In this paper we show that such rigidity phenomena in a closed symplectic manifold M sometimes formally follow from the existence of real-valued functionals with some interesting algebraic properties on the Poisson algebra C ∞ (M). On the one hand, these functionals are related to the notions of quasi-state and quasi-measure (which have been recently called topological measures) on M (see Section 3) which originate in quantum mechanics [1], [2] and have been a subject of intensive study in recent years following the paper [3] by J.F.Aarnes.…”

Section: Introductionmentioning

confidence: 99%

Quasi-states and symplectic intersections

Entov¹,

Polterovich²

2006

Comment. Math. Helv.

136

257

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We establish a link between symplectic topology and a recently emerged branch of functional analysis called the theory of quasi-states and quasi-measures (also known as topological measures). In the symplectic context quasi-states can be viewed as an algebraic way of packaging certain information contained in Floer theory, and in particular in spectral invariants of Hamiltonian diffeomorphisms introduced recently by Yong-Geun Oh. As a consequence we prove a number of new results on rigidity of intersections in symplectic manifolds. This work is a part of a joint project with Paul Biran.

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“…The notion of a quasi-state originates in quantom mechanics [1,2], and has been a subject of intensive study in recent years following the paper [3] by J. F. Aarnes. Here is the definition.…”

Section: Quasi-statementioning

confidence: 99%