Resumen de Decoherence in pre-symmetric spaces

C. Edwards, V. Hügli

• Pre-symmetric complex Banach spaces have been proposed as models for state spaces of physical systems. A structural projection on a pre-symmetric space represents an operation on the corresponding system, and has as its range a further pre-symmetric space which represents the state space of the resulting system and symmetries of the system are represented by elements of the group of linear isometries of . Two structural projections and on the pre-symmetric space represent decoherent operations when their ranges are rigidly collinear. It is shown that, for decoherent elements and of , there exists an involutive element in which conjugates the structural projections corresponding to and , and conditions are found for to exchange and . The results are used to investigate when certain subspaces of are the ranges of contractive projections and, therefore, represent systems arising from filtering operations.