a1 Department of Mathematics, Ufa State Aviation Technical University, Ufa 450000, Russia, e-mail: email@example.com
a2 Department of Mathematical Sciences, 301 Science Engineering Building, University of Arkansas, Fayetteville AR 72701, United States of America, e-mail: firstname.lastname@example.org
We characterise the compact composition operators from any Mobius invariant Banach space to VMOA, the space of holomorphic functions on the unit disk U that have vanishing mean oscillation. We use this to obtain a characterisation of the compact composition operators from the Bloch space to VMOA. Finally, we study some properties of hyperbolic VMOA functions. We show that a function is hyperbolic VMOA if and only if it is the symbol of a compact composition operator from the Bloch space to VMOA.
(Received July 06 1999)