Block representations for classes of isometric operators between Kreĭn spaces (Q2869935)

The behaviour of isometric and unitary operators and relations in Kreĭn spaces is investigated. This is done with the help of so-called archetypical isometric relations. These archetypical relations allow a block decomposition with respect to a hyper-maximal neutral subspace \(\mathcal M\) and \(J\mathcal M\), where \(J\) denotes a fundamental symmetry (unfortunately, the author prefers to use \(j\) as a symbol for a fundamental symmetry). It is shown that the investigation of compositions of unitary operators can be reduced to the study of archetypical unitary operators. Moreover, necessary and sufficient conditions for an isometric operator to be a unitary operator are presented. Finally, these results are used to study quasi-boundary relations and to generalize some results concerning boundary relations for intermediate extensions. Moreover, the strong connection between quasi-boundary triplets and (multi-valued) generalized boundary triplets is investigated.