Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors
We show that all the free Araki–Woods factors Γ ( H R , U t ) ″ have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor N ⊂ Γ ( H R , U t ) ″ which is the range of a normal conditional expectation has no Cartan subalgebra. We fin...
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| Veröffentlicht in: | Advances in mathematics (New York. 1965) 2011-10, Vol.228 (2), p.764-802 |
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| container_title | Advances in mathematics (New York. 1965) |
| container_volume | 228 |
| creator | Houdayer, Cyril Ricard, Éric |
| description | We show that all the free Araki–Woods factors
Γ
(
H
R
,
U
t
)
″
have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor
N
⊂
Γ
(
H
R
,
U
t
)
″
which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III
1 factors constructed by Connes in the ʼ70s can never be isomorphic to any free Araki–Woods factor, which answers a question of Shlyakhtenko and Vaes. |
| doi_str_mv | 10.1016/j.aim.2011.06.010 |
| format | Article |
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Γ
(
H
R
,
U
t
)
″
have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor
N
⊂
Γ
(
H
R
,
U
t
)
″
which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III
1 factors constructed by Connes in the ʼ70s can never be isomorphic to any free Araki–Woods factor, which answers a question of Shlyakhtenko and Vaes.</description><identifier>ISSN: 0001-8708</identifier><identifier>EISSN: 1090-2082</identifier><identifier>DOI: 10.1016/j.aim.2011.06.010</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Cartan subalgebras ; Complete metric approximation property ; Deformation/rigidity ; Free probability ; Functional Analysis ; Mathematics ; Type III factors</subject><ispartof>Advances in mathematics (New York. 1965), 2011-10, Vol.228 (2), p.764-802</ispartof><rights>2011 Elsevier Inc.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c440t-c80827d8663d952c068ff2d7d2b9575dc5a63b325920a455933400566615da33</citedby><cites>FETCH-LOGICAL-c440t-c80827d8663d952c068ff2d7d2b9575dc5a63b325920a455933400566615da33</cites><orcidid>0000-0002-5953-263X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S000187081100199X$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01662170$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Houdayer, Cyril</creatorcontrib><creatorcontrib>Ricard, Éric</creatorcontrib><title>Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors</title><title>Advances in mathematics (New York. 1965)</title><description>We show that all the free Araki–Woods factors
Γ
(
H
R
,
U
t
)
″
have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor
N
⊂
Γ
(
H
R
,
U
t
)
″
which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III
1 factors constructed by Connes in the ʼ70s can never be isomorphic to any free Araki–Woods factor, which answers a question of Shlyakhtenko and Vaes.</description><subject>Cartan subalgebras</subject><subject>Complete metric approximation property</subject><subject>Deformation/rigidity</subject><subject>Free probability</subject><subject>Functional Analysis</subject><subject>Mathematics</subject><subject>Type III factors</subject><issn>0001-8708</issn><issn>1090-2082</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KxDAQgIMouK4-gLdcPbRO0iZt8VQWdYUFLwt6C2l-NOtuU5IqevMdfEOfxJQVj57mh_mGmQ-hcwI5AcIvN7l0u5wCITnwHAgcoBmBBjIKNT1EMwAgWV1BfYxOYtyksilJM0OP7TAE_-52cnS-xykfTBidiVj2Gssuml4Z7C1eyDDKHsfXTm6fTBcktj5gG4zBbZAv7vvz68F7HbGVavQhnqIjK7fRnP3GOVrfXK8Xy2x1f3u3aFeZKksYM1Wn-ypdc17ohlEFvLaW6krTrmEV04pJXnQFZQ0FWTLWFEUJwDjnhGlZFHN0sV_7LLdiCOmP8CG8dGLZrsTUS3I4JRW8kTRL9rMq-BiDsX8AATFZFBuRLIrJogCeUEjM1Z4x6Yc3Z4KIyk1OtAtGjUJ79w_9A_1PeeI</recordid><startdate>20111001</startdate><enddate>20111001</enddate><creator>Houdayer, Cyril</creator><creator>Ricard, Éric</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5953-263X</orcidid></search><sort><creationdate>20111001</creationdate><title>Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors</title><author>Houdayer, Cyril ; Ricard, Éric</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c440t-c80827d8663d952c068ff2d7d2b9575dc5a63b325920a455933400566615da33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Cartan subalgebras</topic><topic>Complete metric approximation property</topic><topic>Deformation/rigidity</topic><topic>Free probability</topic><topic>Functional Analysis</topic><topic>Mathematics</topic><topic>Type III factors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Houdayer, Cyril</creatorcontrib><creatorcontrib>Ricard, Éric</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Advances in mathematics (New York. 1965)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Houdayer, Cyril</au><au>Ricard, Éric</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors</atitle><jtitle>Advances in mathematics (New York. 1965)</jtitle><date>2011-10-01</date><risdate>2011</risdate><volume>228</volume><issue>2</issue><spage>764</spage><epage>802</epage><pages>764-802</pages><issn>0001-8708</issn><eissn>1090-2082</eissn><abstract>We show that all the free Araki–Woods factors
Γ
(
H
R
,
U
t
)
″
have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor
N
⊂
Γ
(
H
R
,
U
t
)
″
which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III
1 factors constructed by Connes in the ʼ70s can never be isomorphic to any free Araki–Woods factor, which answers a question of Shlyakhtenko and Vaes.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.aim.2011.06.010</doi><tpages>39</tpages><orcidid>https://orcid.org/0000-0002-5953-263X</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0001-8708 |
| ispartof | Advances in mathematics (New York. 1965), 2011-10, Vol.228 (2), p.764-802 |
| issn | 0001-8708 1090-2082 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Cartan subalgebras Complete metric approximation property Deformation/rigidity Free probability Functional Analysis Mathematics Type III factors |
| title | Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors |
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