Weighted operator least squares problems and the J-trace in Krein spaces

Abstract

Given B,C and W operators in the algebra L(H) of bounded linear operators on the Krein space H, the minimization problem min (BX − C)^{#}W(BX − C), for X ∈ L(H), is studied when the weight W is selfadjoint. The analogous maximization and min-max problems are also considered. Complete answers to these problems and to those naturally associated to trace clase operators on Krein spaces are given.