  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.
