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

## TL;DR

This paper investigates least squares and trace problems involving operators in Krein spaces, providing comprehensive solutions for weighted minimization, maximization, and min-max problems with selfadjoint weights.

## Contribution

It offers the first complete analysis of weighted least squares and trace problems in Krein spaces, including maximization and min-max formulations.

## Key findings

- Derived explicit solutions for weighted least squares problems.
- Extended results to trace class operators in Krein spaces.
- Provided comprehensive solutions to maximization and min-max problems.

## 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 in 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.