Abstract
The behavior of isometric and unitary operators between Krein spaces is investigated by means of block decompositions. Therefore two types of isometric operators having a block representation, so-called archetypical isometric operators, are introduced. It is shown that interesting classes of isometric operators, in particular the class of unitary operators, can be expressed as a composition of archetypical isometric operators and bounded unitary operators. As a consequence of these block representations, useful information about the behavior of the isometric operators under consideration can be obtained. In particular, some results on (the Weyl families of) (quasi-) boundary triplets are presented. Mathematics subject classification (2010): 47A06, 47B25, 47B50, 47A56.
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