Abstract
A Banach algebra \(\mathcal {A}\) is called weakly regular if its multiplicative semigroup is E-inversive. We show that for a unimodular group G which admits an integrable unitary representation, \(L^1(G)\) is weakly regular. Moreover for a locally compact Abelian group, \(L^1(G)\) is weakly regular if and only if G is compact; while \(L^1(G)^{**}\) is weakly regular if and only if G is finite. All of our results hold, if we replace \(L^1(G)\) with M(G).
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Communicated by Anthony Lau.
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Esslamzadeh, G.H., Fouladi, M. Weak regularity of group algebras. Semigroup Forum 97, 223–228 (2018). https://doi.org/10.1007/s00233-018-9963-0
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DOI: https://doi.org/10.1007/s00233-018-9963-0