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Schrödinger’s Cat Meets Occam’s Razor [PDF]
Entropy, 2022 We discuss V.P. Belavkin’s approach to the Schrödinger cat problem and show its close relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman.
Richard D. Gill
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Causality in Schwinger’s Picture of Quantum Mechanics [PDF]
Entropy, 2022 This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on
Florio M. Ciaglia +5 more
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Lattice isomorphisms between projection lattices of von Neumann algebras
Forum of Mathematics, Sigma, 2020 Generalizing von Neumann’s result on type II $_1$ von Neumann algebras, I characterise lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable ...
Michiya Mori
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Electronic Proceedings in Theoretical Computer Science, 2017 In 1973 Paschke defined a factorization for completely positive maps between C*-algebras. In this paper we show that for normal maps between von Neumann algebras, this factorization has a universal property, and coincides with Stinespring's dilation for ...
Abraham Westerbaan, Bas Westerbaan
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On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables
Comptes Rendus. Mathématique, 2023 Let $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where $-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \lnot \simeq M_0(H_{\mathbb{R}})$ for $-1 < q \ne
Caspers, Martijn
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Derivations of Murray–von Neumann algebras [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2019 AbstractIn this paper, we answer in the affirmative the long-standing conjecture that the first cohomology group of the Murray–von Neumann algebraS(ℳ){S(\mathcal{M})}of all operators affiliated with a typeII1{\mathrm{II}_{1}}von Neumann algebraℳ{\mathcal{M}}is 0. That is, we show that all derivations ofS(ℳ){S(\mathcal{M})}are inner.
Aleksey Ber +2 more
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Derivations with values in noncommutative symmetric spaces
Comptes Rendus. Mathématique, 2023 Let $E=E(0,\infty )$ be a symmetric function space and $E(\mathcal{M},\tau )$ be the noncommutative symmetric space corresponding to $E(0,\infty )$ associated with a von Neumann algebra with a faithful normal semifinite trace.
Huang, Jinghao, Sukochev, Fedor
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On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras
International Journal of Mathematics and Mathematical Sciences, 2020 The relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. C∗-algebras) can be described as significant and influential. Examples of numerous relationships have been established.
F. B. H. Jamjoom, A. H. Al Otaibi
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Orthogonalization of Positive Operator Valued Measures
Comptes Rendus. Mathématique, 2022 We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by Kempe–Vidick and Ji–
de la Salle, Mikael
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Lifting endomorphisms to automorphisms [PDF]
, 2007 Normal endomorphisms of von Neumann algebras need not be extendable to automorphisms of a larger von Neumann algebra, but they always have asymptotic lifts.
Arveson, William, Courtney, Dennis
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