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

Published online by Cambridge University Press:  01 July 2007

C. MARTIN EDWARDS
C. MARTIN EDWARDS*
Affiliation:
The Queen's College, Oxford, OX1 4AW.
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Abstract

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 S∨T majorizing both S and T, and that S, T and S∨T form a compatible family.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 121 - 144
Copyright
Copyright © Cambridge Philosophical Society 2007

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