caa a22 4500 386385432 CHVBK 20180307112056.0 cr unu---uuuuu 161130e198907 xx s 000 0 eng 10.1017/S030500410006802X doi S030500410006802X pii (NATIONALLICENCE)cambridge-10.1017/S030500410006802X Affine structure of facially symmetric spaces [Elektronische Daten] 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. Copyright © Cambridge Philosophical Society 1989 Friedman Yaakov Department of Mathematics, Jerusalem College of Technology, P.O. Box 16031. Jerusalem 91160, Israel Russo Bernard Department of Mathematics, University of California, Irvine, California 92717, U.S.A. Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/1(1989-07), 107-124 0305-0041 106:1<107 1989 106 PSP https://doi.org/10.1017/S030500410006802X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S030500410006802X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Friedman Yaakov Department of Mathematics, Jerusalem College of Technology, P.O. Box 16031. Jerusalem 91160, Israel NATIONALLICENCE 700 1- Russo Bernard Department of Mathematics, University of California, Irvine, California 92717, U.S.A NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/1(1989-07), 107-124 0305-0041 106:1<107 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge