Connes‐Amenability And Normal, Virtual Diagonals For Measure Algebras I

By Volker Runde. Bulletin of the Australian Mathematical Society, 2001

67 citations recorded by the source corpus.

It is proved that the measure algebra M(G) of a locally compact group G is Connes‐amenable if and only if G is amenable.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9477205e9f988ef2b8bbbfc3f282c5289c09d4ef

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In Algebra and Number Theory

1. N. Spronk
2. Ebrahim Samei
3. Ross Stokke
4. Volker Runde
5. Matthew Daws

In Mathematical Physics

1. N. Spronk
2. Ebrahim Samei
3. Ross Stokke
4. Volker Runde
5. Matthew Daws

Citations in the corpus

• Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule (2003, background): “In contrast, it was proven in [20], for a locally compact group G, that M(G) is Connes-amenable – and, equivalently, has a normal, virtual diagonal by [21] – if and only if G is amenable.”
• Biflatness and Pseudo-Amenability of Segal Algebras (2008, background): “the measure algebra M(G) is amenable if and only if Gis both amenable and discrete [6], however M(G) is Connes-amenable (a definition of amenability for dual Banach algebras) exactly when Gis amenable [33]. As another example, the Fourier algebra, A(G), can fail to be amenable even for compact groups”