Unitary orbits of self-adjoint operators in simple <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">Z</mml:mi></mml:math>-stable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math>-algebras

Jacelon, Bhishan; Strung, Karen R.; Toms, Andrew S.

doi:10.1016/j.jfa.2015.08.019

Cited by 9 publications

(12 citation statements)

References 34 publications

(46 reference statements)

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“…Our first use of Cuntz comparison is the following, now-standard consequence of Ciuperca and Elliott's classification of * -homomorphisms from C 0 ((0, 1]) to stable rank one C * -algebras by their Cuntz semigroup data, from [15,Theorem 4] (and extended in [60] and [40]). We shall use this result in Lemma 2.6 to obtain our second Lebesgue trace cone as a unitary conjugate of the first cone.…”

Section: Two Lebesgue Trace Conesmentioning

confidence: 99%

Quasidiagonality of nuclear C^*-algebras

2017

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Abstract. We prove that faithful traces on separable and nuclear C * -algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear C * -algebras of finite nuclear dimension which satisfy the UCT is now complete. Secondly, our result links the finite to the general version of the Toms-Winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension. Finally, we confirm the Rosenberg conjecture: discrete, amenable groups have quasidiagonal C * -algebras.

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Section: Two Lebesgue Trace Conesmentioning

confidence: 99%

Quasidiagonality of nuclear C^*-algebras

2017

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“…Using Cuntz semigroup classification results, one can prove the existence of a nuclear C * -subalgebra B ⊆ A with rather special properties. [64,Theorem 4.1] spells out the properties of B that we need: [43] and [64] involves using these properties to reduce the proof of certain properties of self-adjoint elements in A to the case of self-adjoint elements in B. We we will use the same technique to prove the following theorem.…”

Section: Explicit Constantsmentioning

confidence: 99%

The Dixmier property and tracial states for C⁎-algebras

Archbold

Robert

Tikuisis

2017

Journal of Functional Analysis

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It is shown that a unital C * -algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsidó theorem for simple C * -algebras. We also study a uniform version of the Dixmier property, as satisfied for example by von Neumann algebras and the reduced C * -algebras of Powers groups, but not by all C * -algebras with the Dixmier property, and we obtain necessary and sufficient conditions for a simple unital C * -algebra with unique tracial state to have this uniform property. We give further examples of C * -algebras with the uniform Dixmier property, namely all C * -algebras with the Dixmier property and finite radius of comparison-by-traces. Finally, we determine the distance between two Dixmier sets, in an arbitrary unital C * -algebra, by a formula involving tracial data and algebraic numerical ranges.

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“…This question has been active in other C * -algebras (e.g. [9,15,16,31,35,36,59,60]) where the most recent work has made use of K-theoretic properties and ideas.…”

Section: Introductionmentioning

confidence: 99%

Closed convex hulls of unitary orbits in C⁎-algebras of real rank zero

Skoufranis

2016

Journal of Functional Analysis

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In this paper, we study closed convex hulls of unitary orbits in various C * -algebras. For unital C * -algebras with real rank zero and a faithful tracial state determining equivalence of projections, a notion of majorization describes the closed convex hulls of unitary orbits for self-adjoint operators. Other notions of majorization are examined in these C * -algebras. Combining these ideas with the Dixmier property, we demonstrate unital, infinite dimensional C * -algebras of real rank zero and strict comparison of projections with respect to a faithful tracial state must be simple and have a unique tracial state. Also, closed convex hulls of unitary orbits of self-adjoint operators are fully described in unital, simple, purely infinite C * -algebras.

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Unitary orbits of self-adjoint operators in simple Z-stable C⁎-algebras

Abstract: Abstract. We prove that in a simple, unital, exact, Z-stable C * -algebra of stable rank one, the distance between the unitary orbits of self-adjoint elements with connected spectrum is completely determined by spectral data. This fails without the assumption of Z-stability.

Cited by 9 publications

References 34 publications

Quasidiagonality of nuclear C^*-algebras

Quasidiagonality of nuclear C^*-algebras

The Dixmier property and tracial states for C⁎-algebras

Closed convex hulls of unitary orbits in C⁎-algebras of real rank zero

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