The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (2386 KB) | Metadata | Table of Contents | ZAA summary
Volume 11, Issue 3, 1992, pp. 293–334
DOI: 10.4171/ZAA/604

Published online: 1992-09-30

A Study on the Geometry of Pairs of Positive linear Forms, Algebraic Transition Probability and Geometrical Phase over Non - Commutative Operator Algebras (I)

Peter M. Alberti[1]

(1) Universität Leipzig, Germany

Some aspects in the geometry of pairs of positive linear forms on unital $C*$-algebras are considered. Especially, the geometrical relations among the vector representatives of the forms of such a pair within a representation, where both forms can be realized as vectors simultaneously, are studied and discussed in detail. The results obtained in this part extend early results of H. Araki and are intimately related to such functors like the Bures distance and the algebraic transition probability considered by A. Uhlmann and others. The results will be used to discuss and to investigate sonic extensions of geometrical concepts, which have been found to be of interest recently in Mathematical Physics in context of the problems of the so-called geometrical phase.

Keywords: Functional Analysis, $C*$-Algebras, vN-Algebras, Non-Commutative Probability, Non-Commutative Geometry

Alberti Peter: A Study on the Geometry of Pairs of Positive linear Forms, Algebraic Transition Probability and Geometrical Phase over Non - Commutative Operator Algebras (I). Z. Anal. Anwend. 11 (1992), 293-334. doi: 10.4171/ZAA/604