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. Every L-projection is a neutral GL-projection, and such a projection represents a classical operation. Two neutral GL-projections $R$ and $S$ on the pre-symmetric space $A_*$ represent decoherent operations when their ranges are rigidly collinear. It is shown that if $R$ and $S$ each satisfy a condition, a possible physical interpretation of which is that the information lost in their measurement is partially recoverable, then $R$ and $S$ have as supremum $R + S$ and the operations corresponding to $R$, $S$ and $R+S$ are simultaneously performable. Furthermore, it is shown that the smallest L-projections majorizing $R$, $S$ and $R + S$ coincide, and the greatest L-projection majorized by $R+S$ is identified.

AMS Subject Classification (1991): 46L70, 17C65, 81P15

Keyword(s): ^*, JBW-triple, pre-symmetric space, contractive projection, inner ideal, decoherence

Received January 13, 2006. (Registered under 5918/2009.)