Affine structure of facially symmetric spaces
Yaakov FriedmanDepartment of Mathematics, Jerusalem College of Technology, P.O. Box 16031. Jerusalem 91160, IsraelBernard RussoDepartment of Mathematics, University of California, Irvine, California 92717, U.S.A
1989en
ABI
Abstract
In [ 7 ], the authors proposed the problem of giving a geometric characterization of those Banach spaces which admit an algebraic structure. Motivated by the geometry imposed by measuring processes on the set of observables of a quantum mechanical system, they introduced the category of facially symmetric spaces . A discrete spectral theorem for an arbitrary element in the dual of a reflexive facially symmetric space was obtained by using the basic notions of orthogonality, protective unit, norm exposed face, symmetric face, generalized tripotent and generalized Peirce projection , which were introduced and developed in this purely geometric setting.
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