Global solutions of approximation problems in Krein spaces

Three approximation problems in Krein spaces are studied, namely the indefinite weighted least squares problem and the related problems of indefinite abstract splines and smoothing. In every case, we analyze if the problem has a solution for every point of the Krein space, the existence of a linear and continuous operator that maps each data point to its solution and when the associated operator problem considering the J-trace has a solution.