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Approximate Identities in Spaces of all Absolutely Continuous Measures on Locally Compact Semigroups

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Abstract

Let G be a locally compact group. Then Ma (G), the space of all absolutely continuous measures on G, has a bounded approximate identity. Baker and Baker proved that ℒ(S) (the space of all measures μ ∈ M(S) so that maps x ↦ εx *|μ| and x ↦ |μ|*εx are weak continuous from a locally compact semigroup S into M(S)) is closed under absolutely continuity and has an approximate identity. The main purpose of this paper is to show that similar results hold true for a locally compact semigroup S and Ma(S) the space of all absolutely continuous measures on S.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

    A. Pourabbas & A. Riazi

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  1. A. Pourabbas
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  2. A. Riazi
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Correspondence to A. Pourabbas or A. Riazi.

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Pourabbas, A., Riazi, A. Approximate Identities in Spaces of all Absolutely Continuous Measures on Locally Compact Semigroups. Semigroup Forum 70, 263–268 (2005). https://doi.org/10.1007/s00233-004-0160-y

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  • DOI: https://doi.org/10.1007/s00233-004-0160-y

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