Indefinite least-squares problems and pseudo-regularity

• Published in: Journal of mathematical analysis and applications Vol. 430; no. 2; pp. 895 - 908
• Main Authors: Giribet, Juan Ignacio, Maestripieri, Alejandra, Martínez Pería, Francisco
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-10-2015
• Subjects: Indefinite least-squares; Krein space; Pseudo-regular subspace; Krein space; Pseudo-regular subspace; Indefinite least-squares
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2015.05.015

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]=minx∈H⁡[Cx−y,Cx−y]. The indefinite least-squares problem has been thoroughly studied before under the assumption that the range of C 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.