### 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 result in a new Dirac structure, but in the Hilbert space 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 conposition of Dirac structures to the Redheffer star product of unitary operators.

Original language | Undefined |
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Title of host publication | Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems |

Editors | Y Yamamoto |

Place of Publication | Kyoto |

Publisher | Erasmus University Rotterdam |

Pages | 27-32 |

Number of pages | 6 |

ISBN (Print) | not assigned |

Publication status | Published - 28 Jul 2006 |

Event | 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 - Kyoto, Japan Duration: 24 Jul 2006 → 28 Jul 2006 Conference number: 17 |

### Publication series

Name | |
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Number | supplement |

### Conference

Conference | 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006 |
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Abbreviated title | MTNS |

Country | Japan |

City | Kyoto |

Period | 24/07/06 → 28/07/06 |

### Keywords

- MSC-93C25
- MSC-46C20
- IR-66606
- METIS-237614
- EWI-8148

## Cite this

Kurula, M., van der Schaft, A., & Zwart, H. J. (2006). Composition of infinite-dimensional Dirac structures. In Y. Yamamoto (Ed.),

*Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems*(pp. 27-32). Kyoto: Erasmus University Rotterdam.