The Pisier algebra [Pscr] consists of those continuous functions f on the unit circle [] for which

formula here

is continuous on [] almost surely, that is, for almost every choice of a sequence of signs (±1, ±1, …). In this paper, we prove that spectral synthesis holds in [Pscr]. Moreover, we show that certain closed ideals in [Pscr] with infinite hull have bounded approximate identities and give an example of a closed ideal in [Pscr] which does not have a bounded approximate identity.