Pub Date : 2020-02-27DOI: 10.1017/9781108782081.023
{"title":"Complex interpolation and maximal tensor product","authors":"","doi":"10.1017/9781108782081.023","DOIUrl":"https://doi.org/10.1017/9781108782081.023","url":null,"abstract":"","PeriodicalId":245546,"journal":{"name":"Tensor Products of <I>C</I>*-Algebras and Operator Spaces","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130079953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-27DOI: 10.1017/9781108782081.003
{"title":"Completely bounded and completely positive maps","authors":"","doi":"10.1017/9781108782081.003","DOIUrl":"https://doi.org/10.1017/9781108782081.003","url":null,"abstract":"","PeriodicalId":245546,"journal":{"name":"Tensor Products of <I>C</I>*-Algebras and Operator Spaces","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114510652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-27DOI: 10.1017/9781108782081.017
{"title":"Equivalence with Tsirelson’s problem","authors":"","doi":"10.1017/9781108782081.017","DOIUrl":"https://doi.org/10.1017/9781108782081.017","url":null,"abstract":"","PeriodicalId":245546,"journal":{"name":"Tensor Products of <I>C</I>*-Algebras and Operator Spaces","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125102921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-01DOI: 10.1017/9781108782081.004
G. Pisier
We first recall some classical notation from noncommutative Abstract Harmonic Analysis on an arbitrary discrete group G. We denote by e (and sometimes by eG) the unit element. Let π :G → B(H) be a unitary representation of G. We denote by C∗ π (G) the C∗-algebra generated by the range of π . Equivalently, C∗ π (G) is the closed linear span of π(G). In particular, this applies to the so-called universal representation of G, a notion that we now recall. Let (πj )j∈I be a family of unitary representations of G, say πj :G→ B(Hj ) in which every equivalence class of a cyclic unitary representation ofG has an equivalent copy. Now one can define the “universal” representation UG :G→ B(H) of G by setting UG = ⊕j∈I πj on H = ⊕j∈IHj .
{"title":"C*-algebras of discrete groups","authors":"G. Pisier","doi":"10.1017/9781108782081.004","DOIUrl":"https://doi.org/10.1017/9781108782081.004","url":null,"abstract":"We first recall some classical notation from noncommutative Abstract Harmonic Analysis on an arbitrary discrete group G. We denote by e (and sometimes by eG) the unit element. Let π :G → B(H) be a unitary representation of G. We denote by C∗ π (G) the C∗-algebra generated by the range of π . Equivalently, C∗ π (G) is the closed linear span of π(G). In particular, this applies to the so-called universal representation of G, a notion that we now recall. Let (πj )j∈I be a family of unitary representations of G, say πj :G→ B(Hj ) in which every equivalence class of a cyclic unitary representation ofG has an equivalent copy. Now one can define the “universal” representation UG :G→ B(H) of G by setting UG = ⊕j∈I πj on H = ⊕j∈IHj .","PeriodicalId":245546,"journal":{"name":"Tensor Products of <I>C</I>*-Algebras and Operator Spaces","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134291660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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