Dirac structures and their composition on Hilbert spaces

Dirac structures appear naturally in the study of certain classes of physical models described by partial differential equations (p.d.e.’s). They are the underlying power conserving structures of the p.d.e.’s. We study these structures and their properties from an operator-theoretic point of view. In particular, we find necessary and sufficient conditions for the composition of two Dirac structures to be a Dirac structure and we show that they can be seen as Lagrangian (hyper-maximal neutral) subspaces of Krĕın spaces. Moreover, special emphasis is laid on Dirac structures associated with operator colligations. It turns out that this class of Dirac structures is linked to boundary triplets and that the class is closed under composition. ∗Corresponding author, tel.: +358-50-57