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Approximate amenability of Banach category algebras with application to semigroup algebras

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Abstract

Let C be a small category. Then we consider ℓ 1(C) as the ℓ 1 algebra over the morphisms of C, with convolution product and also consider \(\ell^{1}(\hat{C})\) as the ℓ 1 algebra over the objects of C, with pointwise multiplication. The main purpose of this paper is to show that approximate amenability of ℓ 1(C) implies of \(\ell^{1}(\hat{C})\) and clearly this implies that C has only finitely many objects. Some applications are given, the main one is the characterization of approximate amenability for ℓ 1(S), where S is a Brandt semigroup, which corrects a result of Lashkarizadeh Bami and Samea (Semigroup Forum 71:312–322, 2005).

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Authors and Affiliations

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

    M. Maysami Sadr & A. Pourabbas

Authors
  1. M. Maysami Sadr
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  2. A. Pourabbas
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Correspondence to M. Maysami Sadr.

Additional information

Communicated by Jimmie D. Lawson.

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Sadr, M.M., Pourabbas, A. Approximate amenability of Banach category algebras with application to semigroup algebras. Semigroup Forum 79, 55–64 (2009). https://doi.org/10.1007/s00233-008-9128-7

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  • DOI: https://doi.org/10.1007/s00233-008-9128-7

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