Full paper in PDF format:
$%C. M. Edwards and R. V. Hügli, Decoherence in pre-symmetric spaces, Rev. Mat. Complut. 21 (2008),
no. 1, 219–249.%$
Decoherence in Pre-symmetric Spaces
C. Martin EDWARDS and Remo V. HÜGLI
Received: May 14, 2007
Accepted: October 8, 2007
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.
Key words: JBW
-triple, pre-symmetric space, decoherence, involutive grading,
exchange automorphism.
2000 Mathematics Subject Classification: Primary 46L70; Secondary 17C65, 81P15.