An Introduction To The Classification Of Amenable C<sup>∗</sup>-Algebras

Lin, Huaxin

doi:10.1142/4751

Cited by 143 publications

(259 citation statements)

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“…We need the following lemmas to control the cardinal number of the spectrum for our purpose. The proof is essentially as in [10]. …”

Section: S T /S ) Is a Unitary Of The Formmentioning

confidence: 99%

“…Definition 1.1 (cf. [9], [10] [9], [10]). A unital simple C * -algebra A has tracial rank zero if for any ω A, any δ > 0 and any non-zero element a ∈ A + , there exists a finite dimensional C * -subalgebra B of A with 1 B = p such that…”

Section: Preliminarymentioning

confidence: 99%

“…If a unital simple C * -algebra A has tracial rank zero, then A has the following properties (the reader may be referred to Lin's book [10]):…”

Section: Preliminarymentioning

confidence: 99%

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Entropy for 𝐶*-algebras with tracial rank zero

Okayasu

2010

Proc. Amer. Math. Soc.

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“…We need the following lemmas to control the cardinal number of the spectrum for our purpose. The proof is essentially as in [10]. …”

Section: S T /S ) Is a Unitary Of The Formmentioning

confidence: 99%

Section: Preliminarymentioning

confidence: 99%

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Entropy for 𝐶*-algebras with tracial rank zero

Okayasu

2010

Proc. Amer. Math. Soc.

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“…(e 9.260) It follows from (e 9.249) and (e 9.247) that It follows (for example, Lemma 2.5.4 of [22]) that there exists a projection e in the C * -subalgebra generated by ae ′ a such that e − e ′ < 1/4. (e 9.264) Therefore τ (e) = τ (e ′ ) ≥ rσ for all τ ∈ T (A).…”

Section: Letmentioning

confidence: 99%

Approximate unitary equivalence in simple $C^{*}$-algebras of tracial rank one

Lin

2012

Trans. Amer. Math. Soc.

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Let C be a unital AH-algebra and let A be a unital separable simple C * -algebra with tracial rank no more than one. Suppose that φ, ψ : C → A are two unital monomorphisms. With some restriction on C, we show that φ and ψ are approximately unitarily equivalent if and only ifwhere φ ‡ and ψ ‡ are homomorphisms from U (C)/CU (C) → U (A)/CU (A) induced by φ and ψ, respectively, and where CU (C) and CU (A) are closures of the subgroup generated by commutators of the unitary groups of C and B.A more practical but approximate version of the above is also presented.

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“…It follows (from 2.3.13 of [9], for example) that there is, for each n, a unital completely positive linear map L n : C → A such that…”

Section: Ah-algebrasmentioning

confidence: 99%