Multiplier cocycles of a flow on a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math>-algebra

Kishimoto, Akitaka

doi:10.1016/j.jfa.2005.10.009

Journal of Functional Analysis

2006

DOI: 10.1016/j.jfa.2005.10.009

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Multiplier cocycles of a flow on a C∗-algebra

Akitaka Kishimoto

Abstract: We show that a multiplier cocycle of a flow on a non-unital C * -algebra can be approximated by a norm-continuous cocycle in the strict topology. As an application among others we show that a flow is approximately inner if and only if the restriction of the flow to a full invariant hereditary C * -subalgebra is approximately inner.

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Cited by 2 publications

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The Classification of Rokhlin Flows on $$\mathrm {C}^{*}$$-algebras

Szabó

2020

Commun. Math. Phys.

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We study flows on C * -algebras with the Rokhlin property. We show that every Kirchberg algebra carries a unique Rokhlin flow up to cocycle conjugacy, which confirms a long-standing conjecture of Kishimoto. We moreover present a classification theory for Rokhlin flows on C * -algebras satisfying certain technical properties, which hold for many C * -algebras covered by the Elliott program. As a consequence, we obtain the following further classification theorems for Rokhlin flows. Firstly, we extend the statement of Kishimoto's conjecture to the non-simple case: Up to cocycle conjugacy, a Rokhlin flow on a separable, nuclear, O∞-absorbing C * -algebra is uniquely determined by its induced action on the prime ideal space. Secondly, we give a complete classification of Rokhlin flows on simple classifiable KK-contractible C * -algebras: Two Rokhlin flows on such a C * -algebra are cocycle conjugate if and only if their induced actions on the cone of lower-semicontinuous traces are affinely conjugate. Contents 19 4. O ∞ -absorbing C * -algebras 30 5. Simple KK-contractible algebras 42 References 54

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The Classification of Rokhlin Flows on $$\mathrm {C}^{*}$$-algebras

Szabó

2020

Commun. Math. Phys.

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Quasi-diagonal flows II

Kishimoto¹

2012

MATH. SCAND.

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Two similar notions defined for flows, quasi-diagonality and pseudo-diagonality, are shown to be equivalent; so approximately inner flows on a quasi-diagonal C * -algebra are quasi-diagonal (not just pseudo-diagonal). We define a notion of MF flow which is weaker than quasi-diagonality and study equivalent conditions following Blackadar and Kirchberg's results on MF algebras and we characterize the dual flow of such on the crossed product as a dual MF flow. In the same spirit we introduce a notion of NF flow and show that NF flows are MF flows on nuclear C * -algebras, or equivalently, quasi-diagonal flows on nuclear C * -algebras. We also introduce a notion of strong quasi-diagonality (in parallel with strong quasi-diagonality versus quasi-diagonality for C * -algebras), whose examples contain AF flows.

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Multiplier cocycles of a flow on a C∗-algebra

Cited by 2 publications

References 10 publications

The Classification of Rokhlin Flows on $$\mathrm {C}^{*}$$-algebras

The Classification of Rokhlin Flows on $$\mathrm {C}^{*}$$-algebras

Quasi-diagonal flows II

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