  We prove that the a standard adaptive algorithm for the Taylor-Hood
discretization of the stationary Stokes problem converges with optimal rate.
This is done by developing an abstract framework for indefinite problems which
allows us to prove general quasi-orthogonality proposed in [Carstensen et al.,
2014]. This property is the main obstacle towards the optimality proof and
therefore is the main focus of this work. The key ingredient is a new
connection between the mentioned quasi-orthogonality and $LU$-factorizations of
infinite matrices.
