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

Abstract

AbstractPre-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-projectionsSandTon the pre-symmetric spaceA*are said to be L-orthogonal if for all elementsxinSA*andyinTA*,By studying the algebraic properties of the dual spaceAofA*, which is a JBW*-triple, it is shown that, provided that the orthogonal neutral GL-projectionsSandTsatisfy a certain geometrical condition, there exists a smallest neutral GL-projectionS∨Tmajorizing bothSandT, and thatS,TandS∨Tform a compatible family.