Note on pointwise contractive projections

LetC(X)be the space of real-valued continuous functions on a Hausdorff completely regular topological spaceX. endowed with the compact-open topology. In this paper necessary and sufficient conditions are given for a subspace ofC(X)to be the range of a pointwise contractive projection inC(X).

Contractive projections on Banach space

In this note we prove the uniqueness of a projection onto a given subspace with strictly contractive complement. We also show that, if one completely contractive projection is invariant under another, then the two commute.