Composition of Infinite-Dimensional Linear Dirac-type Structures
نویسندگان
چکیده
Abstract— In this paper, we define the Dirac structure and give some fundamental tools for its study. We then proceed by defining composition of “split Dirac structures”. In the finite-dimensional case, composition of two Dirac structures always results in a new Dirac structure, but in the Hilbertspace setting this result no longer holds. Thus, the problem of finding necessary and sufficient conditions for the composition of two infinite-dimensional Dirac structures to itself be a Dirac structure arises very naturally. The main result of this paper provides these necessary and sufficient conditions. In addition, we give examples and relate composition of Dirac structures to the Redheffer star product of unitary operators.
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