Existence of optimal subspaces in reflexive Banach spaces

F. E. LEVIS; H. H. CUENYA

ANNALS OF FUNCTIONAL ANALYSIS

Duke University Press

Lugar: Masshad; Año: 2015 vol. 6 p. 69 - 77

Given a finite set Y in a  reflexive Banach space F and a family C of closed subspaces of F, we study the problem of finding a subspace W in C that best approximates the data Y in the sense that sum_{f  in Y} d(f,W) = min_{V in C} sum_{f  in Y} d(f,V), where d is the distance function on F. In this paper, we give necessary conditions and sufficient conditions over C for which such a best approximation exists. In particular, when F has finite dimension a characterization on C is given.