Tensor products of C*-algebras and operator spaces: the Connes-Kirchberg problem
"These notes are centered around the equivalence of two major open problems: one formulated by Connes (1976), about traces and ultraproducts of von Neumann algebras, the other one by Kirchberg (1993) about tensor products of C* algebras. This leads us to emphasize the notion of nuclear pair, th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore
Cambridge University Press
2020
|
| Schriftenreihe: | London Mathematical Society student texts
96 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "These notes are centered around the equivalence of two major open problems: one formulated by Connes (1976), about traces and ultraproducts of von Neumann algebras, the other one by Kirchberg (1993) about tensor products of C* algebras. This leads us to emphasize the notion of nuclear pair, that is a pair of C*-algebras admitting a unique tensor product. The main example is the pair (B,C) formed of the algebra B of bounded operators on Hilbert space and the full group C*-algebra C of any free group. This leads naturally to the weak expectation property (WEP) and the local lifting property (LLP), which we extensively study in connection with the more classical notions of nuclearity and exactness, or local reflexivity for C* algebras. We include two new characterizations of the WEP due to Haagerup but unpublished. We show that B fails the LLP and that the minimal tensor product of B with itself fails the WEP. Several properties of random unitary matrices and random permutations play a crucial role. We show the equivalence of the two main questions with a famous open one about Banach spaces and with Tsirelson's well known open problem in quantum information theory"-- |
| Beschreibung: | Literaturverzeichnis: Seiten 470-481 |
| Beschreibung: | x, 484 Seiten 24 cm |
| ISBN: | 9781108479011 9781108749114 |
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| 520 | 3 | |a "These notes are centered around the equivalence of two major open problems: one formulated by Connes (1976), about traces and ultraproducts of von Neumann algebras, the other one by Kirchberg (1993) about tensor products of C* algebras. This leads us to emphasize the notion of nuclear pair, that is a pair of C*-algebras admitting a unique tensor product. The main example is the pair (B,C) formed of the algebra B of bounded operators on Hilbert space and the full group C*-algebra C of any free group. This leads naturally to the weak expectation property (WEP) and the local lifting property (LLP), which we extensively study in connection with the more classical notions of nuclearity and exactness, or local reflexivity for C* algebras. We include two new characterizations of the WEP due to Haagerup but unpublished. We show that B fails the LLP and that the minimal tensor product of B with itself fails the WEP. Several properties of random unitary matrices and random permutations play a crucial role. We show the equivalence of the two main questions with a famous open one about Banach spaces and with Tsirelson's well known open problem in quantum information theory"-- | |
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| id | DE-604.BV047574338 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:31:32Z |
| indexdate | 2024-07-10T09:15:15Z |
| institution | BVB |
| isbn | 9781108479011 9781108749114 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032959878 |
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| physical | x, 484 Seiten 24 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Pisier, Gilles 1950- Verfasser (DE-588)113782268 aut Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem Gilles Pisier (Texas A&M University) Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore Cambridge University Press 2020 x, 484 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 96 Literaturverzeichnis: Seiten 470-481 "These notes are centered around the equivalence of two major open problems: one formulated by Connes (1976), about traces and ultraproducts of von Neumann algebras, the other one by Kirchberg (1993) about tensor products of C* algebras. This leads us to emphasize the notion of nuclear pair, that is a pair of C*-algebras admitting a unique tensor product. The main example is the pair (B,C) formed of the algebra B of bounded operators on Hilbert space and the full group C*-algebra C of any free group. This leads naturally to the weak expectation property (WEP) and the local lifting property (LLP), which we extensively study in connection with the more classical notions of nuclearity and exactness, or local reflexivity for C* algebras. We include two new characterizations of the WEP due to Haagerup but unpublished. We show that B fails the LLP and that the minimal tensor product of B with itself fails the WEP. Several properties of random unitary matrices and random permutations play a crucial role. We show the equivalence of the two main questions with a famous open one about Banach spaces and with Tsirelson's well known open problem in quantum information theory"-- C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Tensorprodukt (DE-588)4059478-6 gnd rswk-swf C*-algebras Operator spaces C-Stern-Algebra (DE-588)4136693-1 s Tensorprodukt (DE-588)4059478-6 s DE-604 London Mathematical Society student texts 96 (DE-604)BV000841726 96 B:DE-89 V:DE-601 pdf/application https://www.gbv.de/dms/tib-ub-hannover/1689343966.pdf Inhaltsverzeichnis |
| spellingShingle | Pisier, Gilles 1950- Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem London Mathematical Society student texts C-Stern-Algebra (DE-588)4136693-1 gnd Tensorprodukt (DE-588)4059478-6 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4059478-6 |
| title | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem |
| title_auth | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem |
| title_exact_search | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem |
| title_exact_search_txtP | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem |
| title_full | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem Gilles Pisier (Texas A&M University) |
| title_fullStr | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem Gilles Pisier (Texas A&M University) |
| title_full_unstemmed | Tensor products of C*-algebras and operator spaces the Connes-Kirchberg problem Gilles Pisier (Texas A&M University) |
| title_short | Tensor products of C*-algebras and operator spaces |
| title_sort | tensor products of c algebras and operator spaces the connes kirchberg problem |
| title_sub | the Connes-Kirchberg problem |
| topic | C-Stern-Algebra (DE-588)4136693-1 gnd Tensorprodukt (DE-588)4059478-6 gnd |
| topic_facet | C-Stern-Algebra Tensorprodukt |
| url | https://www.gbv.de/dms/tib-ub-hannover/1689343966.pdf |
| volume_link | (DE-604)BV000841726 |
| work_keys_str_mv | AT pisiergilles tensorproductsofcalgebrasandoperatorspacestheconneskirchbergproblem |