Indefinite least squares problems and normal projections in Krein spaces

GIRIBET J. I.; ALEJANDRA MAESTRIPIERI; F. MARTÍNEZ PERÍA

Opatija

Conferencia; 4th Naijman Conference; 2015

Given two Krein spaces H and K, a (bounded) closed-range operator C : H → K and a vector y ∈ K, the indefinite least-squares problem consists in finding those vectors u ∈ H such that[Cu−y,Cu−y] = min[Cx−y,Cx−y]. x∈HThe indefinite least-squares problem has been thoroughly studied before, but the usual assumption on the range of C is too strong, say the range is a uniformly J-positive subspace of K. Along this article the range of C is only supposed to be a J-nonnegative pseudo-regular subspace of K.This work is devoted to present a description for the set of solutions of this abstract problem in terms of the family of J-normal projections onto the range of C.