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Spectral synthesis for Banach Algebras II

J. F. Feinstein·D. W. B. Somerset
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Abstract

This paper continues the study of spectral synthesis and the topologies $τ_{\infty}$ and $τ_r$ 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 $τ_{\infty}$. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of $τ_r$.

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J. F. Feinstein, D. W. B. Somerset. 2000-05-12. Spectral synthesis for Banach Algebras II. https://arxiv.org/abs/math/9909149

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