On linear operators extending [pseudo]metrics
  For every closed subset $X$ of a stratifiable [resp. metrizable] space $Y$ we construct a positive linear extension operator $T:R^{X\times X}\to R^{Y\times Y}$ preserving constant functions, bounded functions, continuous functions, pseudometrics, metrics, [resp. dominating metrics, and admissible metrics]. This operator is continuous with respect to each of the three topologies: point-wise convergence, uniform, and compact-open.   An equivariant analog of the above statement is proved as well. 
Taras Banakh and Czeslaw Bessaga
math.GN math.FA math.MG