Niklas Palmberg, Department of Mathematics, Åbo Akademi University, FIN-20500, Åbo, Finland. E-mail address: niklas.palmberg@abo.fi

Spectra of composition operators on BMOA.

Mikael Lindström

It is shown that if ϕ is an univalent self map on the unit disk D, not an automorphism, with a fixed point in D and the essential spectral radius of the composition operator C_{ϕ} on H^{2} is different from zero, then the spectrum of C_{ϕ} on BMOA coincides with \overline{D}. This answers in the affirmative a conjecture by MacCluer and Saxe.