×

Erratum to: “A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal”. (English) Zbl 1305.46044

Summary: In [ibid.. 358, No. 1, 391–402 (2006; Zbl 1098.46037)], we claimed that, for an amenable, non-compact [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.

MSC:

46H20 Structure, classification of topological algebras
43A10 Measure algebras on groups, semigroups, etc.
22A15 Structure of topological semigroups
22A20 Analysis on topological semigroups
43A07 Means on groups, semigroups, etc.; amenable groups
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)

Citations:

Zbl 1098.46037
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Filali, M., On the actions of a locally compact group on some of its semigroup compactifications, Math. Proc. Cambridge Philos. Soc., 143, 1, 25-39 (2007) · Zbl 1123.22003
[2] Ferri, S.; Strauss, D., A note on the \(\mathcal{WAP} \)-compactification and the \(\mathcal{LUC} \)-compactification of a topological group, Semigroup Forum, 69, 1, 87-101 (2004) · Zbl 1057.22002
[3] Hewitt, Edwin; Zuckerman, Herbert S., The \(l_1\)-algebra of a commutative semigroup, Trans. Amer. Math. Soc., 83, 70-97 (1956) · Zbl 0072.12701
[4] Lardy, L. J., On the identity in a measure algebra, Proc. Amer. Math. Soc., 19, 807-810 (1968) · Zbl 0162.19001
[5] Runde, Volker, A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal, Trans. Amer. Math. Soc., 358, 1, 391-402 (electronic) (2006) · Zbl 1098.46037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.