von Neumann Algebra Approach to Quantum Metrics/Quantum Relations.
- 1st ed.
- 1 online resource (153 pages)
- Memoirs of the American Mathematical Society ; v.215 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- A von Neumann Algebra Approach to Quantum Metrics by Greg Kuperberg and Nik Weaver -- Introduction -- Chapter 1. Measurable and quantum relations -- Chapter 2. Quantum metrics -- 2.1. Basic definitions -- 2.2. More definitions -- 2.3. The abelian case -- 2.4. Reflexivity and stabilization -- 2.5. Constructions with quantum metrics -- 2.6. Intrinsic characterization -- Chapter 3. Examples -- 3.1. Operator systems -- 3.2. Graph metrics -- 3.3. Quantum metrics on M2(C) -- 3.4. Quantum Hamming distance -- 3.5. Quantum tori -- 3.6. Hölder metrics -- 3.7. Spectral triples -- Chapter 4. Lipschitz operators -- 4.1. The abelian case -- 4.2. Spectral Lipschitz numbers -- 4.3. Commutation Lipschitz numbers -- 4.4. Little Lipschitz spaces -- Chapter 5. Quantum uniformities -- 5.1. Basic results -- 5.2. Uniform continuity -- Bibliography -- Quantum Relations by Nik Weaver -- Introduction -- Chapter 1. Measurable relations -- 1.1. Basic definitions -- 1.2. Constructions with measurable relations -- 1.3. Conversion to classical relations -- 1.4. Basic results -- 1.5. Measurable metrics -- Chapter 2. Quantum relations -- 2.1. Basic definitions -- 2.2. Constructions with quantum relations -- 2.3. Basic results -- 2.4. The abelian case -- 2.5. Operator reflexivity -- 2.6. Intrinsic characterization -- 2.7. Quantum tori -- Bibliography -- Notation Index -- Subject Index.
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Von Neumann algebras. Metric spaces. Quantum theory.