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${}^{\ast }$-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 ${\tau }_r$.

27 pages plain tex; some explanations added