Orthogonal pairs of weak*-closed inner ideals in a JBW*-triple

• Autores: C. Martin Edwards
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 1, 2007, págs. 121-144
• Idioma: inglés
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• Resumen

  • Pre-symmetric complex Banach spaces have been proposed as models for state spaces of physical systems. A neutral GL-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. Two neutral GL-projections S and T on the pre-symmetric space A* are said to be L-orthogonal if for all elements x in SA* and y in TA*, By studying the algebraic properties of the dual space A of A*, which is a JBW*-triple, it is shown that, provided that the orthogonal neutral GL-projections S and T satisfy a certain geometrical condition, there exists a smallest neutral GL-projection ST majorizing both S and T, and that S, T and ST form a compatible family.