Abstract: Subspace decompositions of finite element spaces based on
-like orthogonal projections play an
important role for the construction and analysis of
multigrid like iterative methods. Recently several authors
proved the equivalence of the associated discrete norms with
the 
-norm. The present report gives an elementary,
self-contained derivation of this result which is based on
the use of 
-functionals known from the theory of
interpolation spaces.
Keywords: multilevel methods, nonuniform meshes, optimal convergence rates.
AMS(MOS) Subject classifications: 65N55, 65N30, 65N50.
Keywords: multilevel methods, nonuniform meshes, optimal convergence rates
MSC: 65N55, 65N30, 65N50