Theory of Operator Algebras III
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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 [36]
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Representations of the Weyl Algebra in Quantum Geometry
Fleischhack, C. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-008-0593-3 · Cited by 183 · see citing works
- Authors
- Takesaki, M.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Takesaki, Masamichi
- Venue
- Encyclopaedia of Mathematical Sciences
- Publisher
- Springer Berlin Heidelberg
- Published
- 2003
- ISSN
- 0938-0396 (ISSN-L)
- OpenAlex
- W4244651418
- Cited by
- 338
- References
- 0
- Citations by year
- 2026: 15 · 2025: 40 · 2024: 21 · 2023: 31 · 2022: 26 · 2021: 19 · 2020: 47 · 2019: 13 · 2018: 7 · 2017: 11 · 2016: 11 · 2015: 14 · 2014: 13 · 2013: 12 · 2012: 13
- FWCI
- 1.42
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Encyclopaedia of mathematical sciences (publishedVersion)
- International Linear Collider (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Banach Space Theory
- Physical Sciences › Mathematics › Applied Mathematics › Holomorphic and Operator Theory
- Keywords
- von Neumann algebras, operator algebras, noncommutative geometry
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