Resumen de On the difficulty of preserving monotonicity via projections and related results

Douglas Mupasiri, Michael Prophet

• A subspace V of a Banach space X is said to be complemented if there exists a (bounded) projection mapping X onto V . Obviously all subspaces of finitedimension are complemented. The goal of this note is to show that there are (relatively) few monotonically complemented subspaces of finite-dimension in X = (C[a, b], ·∞); that is, finite-dimensional subspaces V ⊂ X for which there exists a projection P : X → V such that P f is monotone-increasing whenever f is. We obtain several corollaries from this consideration, including a result describing the difficulty of preserving n-convexity via a projection.