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Ideal Structure and Stable Rank of \({\mathbb {C} e+ \ell^2(I)}\) with the Hadamard Product

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Abstract

Let I be any index set. We consider the Banach algebra \({\mathbb {C} e+ \ell^2(I)}\) with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize divisors, maximal ideals, closed ideals and closed principal ideals. For \({I=\mathbb {N}}\) we also characterize all prime z-ideals in this Banach algebra.

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Authors and Affiliations

  1. Fachbereich Allgemeinwissenschaften, Georg-Simon-Ohm-Hochschule Nürnberg, Kesslerplatz 12, 90489, Nuremberg, Germany

    Rudolf Rupp

  2. Mathematics Department, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    Amol Sasane

Authors
  1. Rudolf Rupp
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  2. Amol Sasane
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Correspondence to Amol Sasane.

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Communicated by Daniel Alpay.

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Rupp, R., Sasane, A. Ideal Structure and Stable Rank of \({\mathbb {C} e+ \ell^2(I)}\) with the Hadamard Product. Complex Anal. Oper. Theory 4, 881–899 (2010). https://doi.org/10.1007/s11785-009-0027-z

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  • DOI: https://doi.org/10.1007/s11785-009-0027-z

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