  In the first part of this paper, we establish a conditional optimality result
for an adaptive mixed finite element method for the stationary Stokes problem
discretized by the standard Taylor-Hood elements, under the assumption of the
so-called general quasi-orthogonality. Optimality is measured in terms of a
modified approximation class defined through the total error, as is customary
since the seminal work of Cascon, Kreuzer, Nochetto and Siebert. The second
part of the paper is independent of optimality results, and concerns
interrelations between the modified approximation classes and the standard
approximation classes (the latter defined through the energy error). Building
on the tools developed in the papers of Binev, Dahmen, DeVore, and Petrushev,
and of Gaspoz and Morin, we prove that the modified approximation class
coincides with the standard approximation class, modulo the assumption that the
data is regular enough in an appropriate scale of Besov spaces.
