Abstract.
This paper continues the study of spectral synthesis and the topologies \(\tau_{\infty}\) and \(\tau_r\) on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C\(^*\)-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of \(\tau_{\infty}\). Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of \(\tau_r\).
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Received: 6 October 1999; in final form: 15 May 2000 / Published online: 25 June 2001
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Feinstein, J., Somerset, D. Spectral synthesis for Banach algebras, II. Math Z 239, 183–213 (2002). https://doi.org/10.1007/s002090100291
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DOI: https://doi.org/10.1007/s002090100291