The invariant subspace problem, which is one of the most funda mental questions in operator theory and which has been a subject of study for
several decades remains open even on a Hilbert space. However, for certain
classes of operators, for example, compact operators, solutions do exist. In this
paper, we address this question for contractive operators T defined on a Krein
space K. We investigate the existence of semi-definite invariant subspaces and
establish that every contractive operator T defined on a Krein space K has
maximal semi-definite invariant subspaces
