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Affine structure of facially symmetric spaces

Published online by Cambridge University Press:  24 October 2008

Yaakov Friedman  and
Bernard Russo
Yaakov Friedman
Affiliation:
Department of Mathematics, Jerusalem College of Technology, P.O. Box 16031. Jerusalem 91160, Israel
Bernard Russo
Affiliation:
Department of Mathematics, University of California, Irvine, California 92717, U.S.A.
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 107 - 124
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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