 | Kuperberg G. A Von Neumann algebra approach to quantum metrics / G.Kuperberg, N.Weaver. Quantum relations / N.Weaver. - Providence: American Mathematical Society, 2012. - v, 140 p. - (Memoirs of the American Mathematical Society; vol.215, N 1010). - Bibliogr.: p.131. - Sub. ind.: p.135-140. - ISSN 0065-9266; ISBN 978-0-8218-5341-2
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A von Neumann Algebra Approach to Quantum Metrics by Greg
Kuperberg and Nik Weaver ........................................ 1
Introduction .................................................... 3
Chapter 1 Measurable and quantum relations ..................... 7
Chapter 2 Quantum metrics ..................................... 11
2.1 Basic definitions ......................................... 11
2.2 More definitions .......................................... 14
2.3 The abelian case .......................................... 21
2.4 Reflexivity and stabilization ............................. 24
2.5 Constructions with quantum metrics ........................ 25
2.6 Intrinsic characterization ................................ 33
Chapter 3 Examples ............................................ 37
3.1 Operator systems .......................................... 37
3.2 Graph metrics ............................................. 39
3.3 Quantum metrics on M2(C) .................................. 39
3.4 Quantum Hamming distance .................................. 40
3.5 Quantum tori .............................................. 43
3.6 Holder metrics ............................................ 47
3.7 Spectral triples .......................................... 48
Chapter 4 Lipschitz operators ................................. 53
4.1 The abelian case .......................................... 53
4.2 Spectral Lipschitz numbers ................................ 56
4.3 Commutation Lipschitz numbers ............................. 64
4.4 Little Lipschitz spaces ................................... 69
Chapter 5 Quantum uniformities ................................ 73
5.1 Basic results ............................................. 73
6.1 Uniform continuity ........................................ 75
Bibliography ................................................... 79
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