Examples of Nonlinear Continuous Tensor Products of Measure Spaces and Non-Fock Factorizations

DOI10.1142/S0129055X98000045zbMath0912.46022OpenAlexW2092451619WikidataQ114073235 ScholiaQ114073235MaRDI QIDQ4213201

Anatoly M. Vershik, B. S. Tsirel'son

Publication date: 13 October 1998

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129055x98000045

zbMATH Keywords

filtrationsrandom objectscontinuous tensor product of measure spacescontinuous tensor products of Hilbert spacesHilbert factorizationinverse limit constructionsmeasure space factorizationmeasures on flabby sheavesnets of Borel spacesnonlinear generalizations of random processes with independent valuesnonlinearity and continuity of factorizationsnonlinearizable factorization

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Spaces of operators; tensor products; approximation properties (46B28) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Representation theory of linear operators (47A67) Tensor products in functional analysis (46M05)

Related Items (10)

Boolean functions: influence, threshold and noise ⋮ The Poisson model of the Fock space and representations of current groups ⋮ Simulation example of a black noise ⋮ Noise as a Boolean algebra of \(\sigma\)-fields ⋮ Oded Schramm's contributions to noise sensitivity ⋮ On the scaling limits of planar percolation ⋮ Wave noise: A nonlinear analog of the white noise ⋮ A simple example of black noise ⋮ Integral models of unitary representations of current groups with values in semidirect products ⋮ Dynamics and endogeny for recursive processes on trees

Cites Work

• A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
• Decomposable processes and continuous products of probability spaces
• Decreasing sequences of \(\sigma\)-fields and a measure change for Brownian motion. I
• On rings of operators
• Meyer's theorem on predictability
• Complete Boolean algebras of type I factors
• Quelques applications de la formule de changement de variables pour les semimartingales

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