Spectral synthesis for Banach Algebras II

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 $\tau_r$.