Indefinite least-squares problems and pseudo-regularity

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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2015 vol. 423 p. 895 - 908

0022-247X

Given two Krein spaces $HH$ and $KK$, a (bounded) closed-range operator $C : HH a KK$ and a vector $y in KK$, the indefinite least-squares problem consists in finding those vectors $u inHH$ such that [ K{Cu - y}{Cu - y} = min_{xinHH}K{Cx - y}{Cx - y}. ] The 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 $KK$. Along this article the range of $C$ is only supposed to be a $J$-nonnegative pseudo-regular subspace of $KK$. 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 $C$.