Locally trivial W∗-bundles

Evington, Samuel; Pennig, Ulrich

doi:10.1142/s0129167x16500889

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…Proposition 2.14 (cf. Proposition 3.1 of [6], Lemma 4.2 (ii) of [28] and Proposition 4.3.6 of [12]). Let A be a separable C * -algebra with QT (A) = ∅ and K ⊂ ∂ e (QT (A)) a compact subset.…”

Section: )mentioning

confidence: 99%

Hereditary uniform property $Γ$

Lin¹

2022

Preprint

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We study the uniform property Γ for separable simple C * -algebras which have quasitraces and may not be exact. We show that a stably finite separable simple C * -algebra A with strict comparison and uniform property Γ has tracial approximate oscillation zero and stable rank one. Moreover in this case, its hereditary C * -subalgebras also have a version of uniform property Γ. If a separable non-elementary simple amenable C * -algebra A with strict comparison has this hereditary uniform property Γ, then A is Z-stable.

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Section: )mentioning

confidence: 99%

Hereditary uniform property $Γ$

Lin¹

2022

Preprint

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“…We work in a slightly more general setting than in the introduction to this paper, allowing uniform trace norms with respect to subsets of the trace simplex. General references for the material in this subsection are [38,24,8].…”

Section: Uniform Trace Norms and Uniform Tracial Completionsmentioning

confidence: 99%

Nuclear dimension of extensions of O∞-stable algebras

Evington¹

2022

J. Operator Theory

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“…In this note we investigate W * -bundles from a more abstract point of view, as a class in its own right, with an approach closer to that in [EP16,Evi18]. The main motivation for the present paper is the forthcoming work on tracially complete C * -algebras [CCE + ] by Carrión, Castillejos, Evington, Gabe, Schafhauser, Tikuisis and White.…”

Section: Introductionmentioning

confidence: 99%

Ultraproducts of factorial $W^*$-bundles

Vaccaro¹

2023

Preprint

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This paper investigates factorial W * -bundles and their ultraproducts. More precisely, a W * -bundle is factorial if the von Neumann algebras associated to its fibers are all factors. Let M be the tracial ultraproduct of a family of factorial W * -bundles over compact Hausdorff spaces with finite, uniformly bounded covering dimensions. We prove that in this case the set of limit traces in M is weak * -dense in the trace space T (M). This in particular entails that M is factorial. We also provide, on the other hand, an example of ultraproduct of factorial W * -bundles which is not factorial. Finally, we obtain some results of model-theoretic nature: if A and B are exact, Z-stable C *algebras, or if they both have strict comparison, then A ≡ B implies that T (A) is Bauer if and only if T (B) is. If moreover both T (A) and T (B) are Bauer simplices and second countable, then the sets of extreme traces ∂eT (A) and ∂eT (B) have the same covering dimension.

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Locally trivial W∗-bundles

Cited by 5 publications

References 25 publications

Hereditary uniform property $Γ$

Hereditary uniform property $Γ$

Nuclear dimension of extensions of O∞-stable algebras

Ultraproducts of factorial $W^*$-bundles

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