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A completely bounded non-commutative Choquet boundary for operator spaces 算子空间的完全有界非交换Choquet边界
arXiv: Operator Algebras Pub Date : 2017-03-08 DOI: 10.1093/IMRN/RNX335
Raphael Clouatre, Christopher Ramsey
{"title":"A completely bounded non-commutative Choquet boundary for operator spaces","authors":"Raphael Clouatre, Christopher Ramsey","doi":"10.1093/IMRN/RNX335","DOIUrl":"https://doi.org/10.1093/IMRN/RNX335","url":null,"abstract":"We develop a completely bounded counterpart to the non-commutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we isolate the subset of completely bounded linear maps on an operator space admitting a dilation of the same norm which is multiplicative on the generated $C^*$-algebra. We view such maps as analogues of the familiar unital completely contractive maps, and we exhibit many of their structural properties. Of particular interest to us are those maps which are extremal with respect to a natural dilation order. We establish the existence of extremals and show that they have a certain unique extension property. In particular, they give rise to $*$-homomorphisms which we use to associate to any representation of an operator space an entire scale of $C^*$-envelopes. We conjecture that these $C^*$-envelopes are all $*$-isomorphic, and verify this in some important cases.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125849192","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}
引用次数: 3
Isometries of perfect norm ideals of compact operators 紧算子的完全范数理想的等距
arXiv: Operator Algebras Pub Date : 2017-03-05 DOI: 10.4064/SM170306-19-4
B. Aminov, V. Chilin
{"title":"Isometries of perfect norm ideals of compact operators","authors":"B. Aminov, V. Chilin","doi":"10.4064/SM170306-19-4","DOIUrl":"https://doi.org/10.4064/SM170306-19-4","url":null,"abstract":"It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $mathcal C_Eneq mathcal C_2$ of compact operators, acting in a complex separable infnite-dimensional Hilbert space $mathcal H$ there exist unitary operators $u$ and $v$ on $mathcal H$ such that $V(x)=uxv$ or $V(x) = ux^tv$ for all $xin mathcal C_E$, where $x^t$ is the transpose of an operator $x$ with respect to a fixed orthonormal basis in $mathcal H$. In addition, it is shown that any surjective 2-local isometry on a perfect Banach symmetric ideal $mathcal C_E neq mathcal C_2$ is a linear isometry on $mathcal C_E$.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129706277","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}
引用次数: 4
Non-commutative rational function in strongly convergent random variables 强收敛随机变量中的非交换有理函数
arXiv: Operator Algebras Pub Date : 2017-02-23 DOI: 10.22034/aot.1702-1126
Sheng Yin
{"title":"Non-commutative rational function in strongly convergent random variables","authors":"Sheng Yin","doi":"10.22034/aot.1702-1126","DOIUrl":"https://doi.org/10.22034/aot.1702-1126","url":null,"abstract":"Random matrices like GUE, GOE and GSE have been studied for decades and have been shown that they possess a lot of nice properties. In 2005, a new property of independent GUE random matrices is discovered by Haagerup and Thorbj{o}rnsen in their paper [18], it is called strong convergence property and then more random matrices with this property are followed (see [27], [5], [1], [24], [10] and [3]). In general, the definition can be stated for a sequence of tuples over some text{C}^{ast}-algebras. And in this general setting, some stability property under reduced free product can be achieved (see Skoufranis [30] and Pisier [26]), as an analogy of the result by Camille Male [24] for random matrices. \u0000In this paper, we want to show that, for a sequence of strongly convergent random variables, non-commutative polynomials can be extended to non-commutative rational functions under certain assumptions. Roughly speaking, the strong convergence property is stable under taking the inverse. As a direct corollary, we can conclude that for a tuple (X_{1}^{left(nright)},cdots,X_{m}^{left(nright)}) of independent GUE random matrices, r(X_{1}^{left(nright)},cdots,X_{m}^{left(nright)}) converges in trace and in norm to r(s_{1},cdots,s_{m}) almost surely, where r is a rational function and (s_{1},cdots,s_{m}) is a tuple of freely independent semi-circular elements which lies in the domain of r.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126776110","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}
引用次数: 7
Ore's theorem on cyclic subfactor planar algebras and beyond 关于循环子因子平面代数及其他代数的Ore定理
arXiv: Operator Algebras Pub Date : 2017-02-07 DOI: 10.2140/pjm.2018.292.203
S. Palcoux
{"title":"Ore's theorem on cyclic subfactor planar algebras and beyond","authors":"S. Palcoux","doi":"10.2140/pjm.2018.292.203","DOIUrl":"https://doi.org/10.2140/pjm.2018.292.203","url":null,"abstract":"Ore proved that a finite group is cyclic if and only if its subgroup lattice is distributive. Now, since every subgroup of a cyclic group is normal, we call a subfactor planar algebra cyclic if all its biprojections are normal and form a distributive lattice. The main result generalizes one side of Ore's theorem and shows that a cyclic subfactor is singly generated in the sense that there is a minimal 2-box projection generating the identity biprojection. We conjecture that this result holds without assuming the biprojections to be normal, and we show that it is true for small lattices. We finally exhibit a dual version of another theorem of Ore and a non-trivial upper bound for the minimal number of irreducible components for a faithful complex representation of a finite group.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116620356","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}
引用次数: 8
Free quantitative fourth moment theorems on Wigner space Wigner空间上的自由定量四矩定理
arXiv: Operator Algebras Pub Date : 2017-01-19 DOI: 10.1093/IMRN/RNX036
S. Bourguin, Simon Campese
{"title":"Free quantitative fourth moment theorems on Wigner space","authors":"S. Bourguin, Simon Campese","doi":"10.1093/IMRN/RNX036","DOIUrl":"https://doi.org/10.1093/IMRN/RNX036","url":null,"abstract":"We prove a quantitative Fourth Moment Theorem for Wigner integrals of any order with symmetric kernels, generalizing an earlier result from Kemp et al. (2012). The proof relies on free stochastic analysis and uses a new biproduct formula for bi-integrals. A consequence of our main result is a Nualart-Ortiz-Latorre type characterization of convergence in law to the semicircular distribution for Wigner integrals. As an application, we provide Berry-Esseen type bounds in the context of the free Breuer-Major theorem for the free fractional Brownian motion.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117353266","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}
引用次数: 5
The primitive ideal space of the partial-isometric crossed product of a system by a single automorphism 单自同构系统的部分等距叉积的原始理想空间
arXiv: Operator Algebras Pub Date : 2017-01-16 DOI: 10.1216/RMJ-2017-47-8-2699
W. Lewkeeratiyutkul, Saeid Zahmatkesh
{"title":"The primitive ideal space of the partial-isometric crossed product of a system by a single automorphism","authors":"W. Lewkeeratiyutkul, Saeid Zahmatkesh","doi":"10.1216/RMJ-2017-47-8-2699","DOIUrl":"https://doi.org/10.1216/RMJ-2017-47-8-2699","url":null,"abstract":"Let $(A,alpha)$ be a system consisting of a $C^*$-algebra $A$ and an automorphism $alpha$ of $A$. We describe the primitive ideal space of the partial-isometric crossed product $Atimes_{alpha}^{textrm{piso}}mathbb{N}$ of the system by using its realization as a full corner of a classical crossed product and applying some results of Williams and Echterhoff.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132395144","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}
引用次数: 6
Around trace formulas in non-commutative integration 非交换积分中的迹公式
arXiv: Operator Algebras Pub Date : 2017-01-15 DOI: 10.4171/PRIMS/54-1-7
S. Yamagami
{"title":"Around trace formulas in non-commutative integration","authors":"S. Yamagami","doi":"10.4171/PRIMS/54-1-7","DOIUrl":"https://doi.org/10.4171/PRIMS/54-1-7","url":null,"abstract":"Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula is then applied to explore a variation of Haagerup's trace formula.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124492070","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}
引用次数: 1
Coaction functors, II 协同函子，2
arXiv: Operator Algebras Pub Date : 2017-01-08 DOI: 10.2140/pjm.2018.293.301
S. Kaliszewski, M. B. Landstad, John Quigg
{"title":"Coaction functors, II","authors":"S. Kaliszewski, M. B. Landstad, John Quigg","doi":"10.2140/pjm.2018.293.301","DOIUrl":"https://doi.org/10.2140/pjm.2018.293.301","url":null,"abstract":"In further study of the application of crossed-product functors to the Baum-Connes Conjecture, Buss, Echterhoff, and Willett introduced various other properties that crossed-product functors may have. Here we introduce and study analogues of these properties for coaction functors, making sure that the properties are preserved when the coaction functors are composed with the full crossed product to make a crossed-product functor. The new properties for coaction functors studied here are functoriality for generalized homomorphisms and the correspondence property. We particularly study the connections with the ideal property. The study of functoriality for generalized homomorphisms requires a detailed development of the Fischer construction of maximalization of coactions with regard to possibly degenerate homomorphisms into multiplier algebras. We verify that all \"KLQ\" functors arising from large ideals of the Fourier-Stieltjes algebra $B(G)$ have all the properties we study, and at the opposite extreme we give an example of a coaction functor having none of the properties.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131270756","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}
引用次数: 7
The K-theory of the flip automorphisms 翻转自同构的k理论
arXiv: Operator Algebras Pub Date : 2017-01-08 DOI: 10.2969/aspm/08010123
Masaki Izumi
{"title":"The K-theory of the flip automorphisms","authors":"Masaki Izumi","doi":"10.2969/aspm/08010123","DOIUrl":"https://doi.org/10.2969/aspm/08010123","url":null,"abstract":"We give an algorithm to compute the $K$-groups of the crossed product by the flip automorphism for a nuclear C$^*$-algebra satisfying the UCT.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132596815","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}
引用次数: 5
Functors induced by Cauchy extension of C*-algebras C*-代数的Cauchy扩展诱导的函子
arXiv: Operator Algebras Pub Date : 2017-01-05 DOI: 10.22130/SCMA.2018.73698.306
K. Nourouzi, A. Reza
{"title":"Functors induced by Cauchy extension of C*-algebras","authors":"K. Nourouzi, A. Reza","doi":"10.22130/SCMA.2018.73698.306","DOIUrl":"https://doi.org/10.22130/SCMA.2018.73698.306","url":null,"abstract":"In this paper we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by a non-unital C$^ast$-algebra $mathfrak{F}(mathcal{A})$. Some properties of these functors are also given. In particular, we show that the functors $[cdot]_K$ and $mathfrak{F}$ are exact and the functor $mathfrak{P}$ is normal exact.","PeriodicalId":351745,"journal":{"name":"arXiv: Operator Algebras","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122480278","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}
引用次数: 5
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