Erratum to “A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal”

Runde, Volker

doi:10.1090/S0002-9947-2014-06430-1

Erratum to “A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal”
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Trans. Amer. Math. Soc. 367 (2015), 751-754 Request permission

Abstract:

In Trans. Amer. Math. Soc., vol. 358 (2006), pp. 391–402, we claimed that, for an amenable, non-compact $[\mathrm {SIN}]$-group $G$, the dual Banach algebra $\mathcal {WAP}(G)^\ast$ is Connes-amenable, but lacks a normal virtual diagonal. The proof presented contains a gap. In this erratum, we indicate how the faulty proof can be repaired.

References

M. Filali, On the actions of a locally compact group on some of its semigroup compactifications, Math. Proc. Cambridge Philos. Soc. 143 (2007), no. 1, 25–39. MR 2340973, DOI 10.1017/S0305004107000242
S. Ferri and D. Strauss, A note on the $\scr {WAP}$-compactification and the $\scr {LUC}$-compactification of a topological group, Semigroup Forum 69 (2004), no. 1, 87–101. MR 2063981, DOI 10.1007/s00233-003-0026-8
Edwin Hewitt and Herbert S. Zuckerman, The $l_1$-algebra of a commutative semigroup, Trans. Amer. Math. Soc. 83 (1956), 70–97. MR 81908, DOI 10.1090/S0002-9947-1956-0081908-4
L. J. Lardy, On the identity in a measure algebra, Proc. Amer. Math. Soc. 19 (1968), 807–810. MR 227782, DOI 10.1090/S0002-9939-1968-0227782-8
Volker Runde, A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal, Trans. Amer. Math. Soc. 358 (2006), no. 1, 391–402. MR 2171239, DOI 10.1090/S0002-9947-05-03827-4