Contractive Projections onto Subsets of Lp-Spaces
Per Enflo · 2020
In this paper we will characterize the subsets of (real) L p = L p (0,1), 1 < p < ∞, which are ranges of contractive, possibly non-linear, projections, i.e. projections that satisfy ||Ρ# — Py\\ < \\x — y II for all × and y. We call these sets contractive sets. Similar problems — both linear and non-linear — have earlier been studies in a number of papers.,