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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 401
Twisted duality of the CAR-Algebra H. Baumgärtel, M. Jurke and F. Lledo
We give a complete proof of the twisted duality property $M (q)'= ilde{Z} M (q^perp) ilde{Z}^*$ of the (self--dual) CAR--Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use Modular Theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof.
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