Operator Algebras and Quantum Statistical Mechanics 1
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Every non-degenerate representation π of A(W, μ) on a Hilbert space H has a first-step decomposition: there are measures μν on X such that π|C(X) is unitarily equivalent to the direct sum of canonical multiplication representations on L2(X, μν), and the measures may be chosen so that equal measures correspond to equivalent representations.
“Then there are measures µ ν on X with ν running over some (not necessarily countable) index set N, such that π | C(X ) is unitarily equivalent to the direct-sum representation ν π µ ν , where π µ ν denotes the canonical representation of C(X ) on L 2 (X, µ ν ) by multiplication operators.”
From Representations of the Weyl Algebra in Quantum Geometry (2009) · cites this paper as [12]
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Representations of the Weyl Algebra in Quantum Geometry
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The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation
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- Authors
- Bratteli, O., & Robinson, D. W.
- Affiliations
- University of Oslo (NO)
- Australian National University (AU)
- ORCID
- Robinson, Derek W.
- Venue
- Springer eBooks
- Publisher
- Springer Berlin Heidelberg
- Published
- 1987
- OpenAlex
- W4300128422
- Cited by
- 788
- References
- 0
- Citations by year
- 2026: 38 · 2025: 38 · 2024: 39 · 2023: 37 · 2022: 53 · 2021: 36 · 2020: 29 · 2019: 59 · 2018: 39 · 2017: 31 · 2016: 32 · 2015: 30 · 2014: 24 · 2013: 20 · 2012: 23
- FWCI
- 1.64
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Springer eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Mathematics › Applied Mathematics › Holomorphic and Operator Theory
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Banach Space Theory
- Keywords
- operator algebras, quantum statistical mechanics, von Neumann algebras, C*-algebras, mathematical physics
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