Spectral Analysis in Krein Spaces

Abstract

For a bounded #-unitary, the existence of a Tomita's triangular matrix representation is equivalent to the existence of an invariant maximal nonnegative subspace due to Pontrjagin, Krein et al. In other words, if a bounded #-unitary u has such an invariant subspace, its spectral analysis can be reduced to the following three cases: (i) u is #-spectral; (ii) u is quasi-#-spectral; and (iii) u is represented in the form of a Tomita's triangular matrix.