C*-Algebras and Finite-Dimensional Approximations

By Nathanial P. Brown Narutaka Ozawa. 2008

1,406 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9e4bf8723c94ac1f9aae522985b0924c48f3a306

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In Computational Theory and Mathematics

Citations in the corpus

Strong solidity of group factors from lattices in SO(n,1) and SU(n,1) (2010, background): “We now need only show (2) ⇒ (3) as (3) ⇒ (2) is trivial.”
A classification of finite simple amenable Z-stable C*-algebras, II, --C*-algebras with rational generalized tracial rank one (2019, background): “3 of [4] again, the tensor product map”
Annular representation theory for rigid $C^{*}$-tensor categories (2015, background): “exists a faithful D-class representation ˇof C (A 0;0). Taking innite direct sums if necessary, we can assume that ˇ(C (A 0;0)) contains no compact operators. Then by Glimm’s Lemma (see, for example [6], Lemma 1.4.11 ), for any state ˚of C (A 0;0) there exists a sequence of vector states ! n !˚. By”
Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, background): “5, the main result of [68], and the fact that finite decomposition rank (a refinement of the completely positive approximation property) implies nuclearity (see [10]).”
Topological dynamical systems associated to II1-factors (2010, background): “[2]) and B is an ultraproduct II1-factor, then Hom(A,B) can be identified with the tracial state space T(A) of A; see [14, Corollary 3.”
Noncommutative $L^{p}$-spaces without the completely bounded approximation property (2010, background): “For equivalent formulation of exactness for a group, see [4], Chapter 5.”
The ideal structure of reduced crossed products (2008, background): “For an introduction to crossed products we refer to [3, 21].”
Riesz and frame systems generated by unitary actions of discrete groups (2014, background): “This general setting is widely accepted and very well understood in noncommutative geometry and operator algebra [8, 6].”
Weak Amenability of Hyperbolic Groups (2007, background): “nite or inﬁnite sequence of points in Γ such that d(p(m),p(n)) = |m − n| for every m,n. Most of the time, we view a geodesic path pas a subset of Γ. We note the following fact (see e.g., Lemma E.8 in [BO]). Lemma 5. Let Γ be a connected graph. Then, for any inﬁnite geodesic path p: N0 → Γ and any x ”