Nuclear C*-Algebras

By M. Takesaki. 2003

147 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/36047165ebd9e889d486c7a2e140ee9289733bb8

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The weak expectation property was introduced by Lance in[79].”
Nuclearity Related Properties in Operator Systems (2011, background): “Another important aspect of the maximal tensor product is the following duality property given by Lance in [29]: A linear map f : S ⊗max T → C is positive if and only if the corresponding map φf : S → T d is completely positive.”
Property A, partial translation structures, and uniform embeddings in groups (2006, background): “For example, a discrete group G is amenable if and only if the full C∗-algebra C∗(G) is nuclear [7].”
On C -algebras associated with C -correspondences (2003, unknown): “homomorphism ι ⊗max idD: B0 ⊗max D → B ⊗max D by [ L1 , Theorem 3.3].”
L 2 -Invariants of Regular Coverings of Compact Manifolds and CW-Complexes (2001, background): “A group Γ is amenable if and only if the reduced C∗- algebra of Γ is nuclear [139].”
Tensor products of operator systems (2009, methodology): “Except for the last conclusion, the following result is a consequence of the deep work of Choi, Effros, and Lance (see [3], [4], [5], and [7]).”
Crossed products of C*-algebras (2007, background): “Lance has proved that for a discrete group G, C r (G) is nuclear if and only if G is amenable [97].”
Characterisations of the weak expectation property (2013, methodology): “One major motivation for the desire to obtain such a plethora of characterisations of WEP are the results of Kirchberg, who proved that Connes’ embedding conjecture is equivalent to determining if certain C*-algebras have WEP.”