Decoherence in pre-symmetric spaces

• Autores: C. Edwards, V. Hügli
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 21, Nº 1, 2008, págs. 219-249
• Idioma: inglés
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• Resumen

  • 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.