Textbook in PDF format

The Advanced Study Institute on "Foundations of Quantum Mechanics and Ordered Linear Spaces" has been held at Marburg, Federal Republic of Germany, from March 26th to April 6th 1973.
Mathematicians and physicists participated in the meeting. The lectures of the Institute were intended to prepare a common basis for discussions between mathematicians and physicists and for future research on foundations of quantum mechanics by ordered linear spaces. A series of lectures ("Course") provided a coherent introduction into the field of ordered normed vector spaces and their application to the foundation of quantum mechanics. Additional lectures treated special mathematical and physical topics, which were in more or less close connection to the lectures of the course.
The present volume contains the notes of the lectures revised by the authors.
Orderings of vector spaces
Duality of cones in locally convex spaces
Order unit and base norm spaces
Minimal decompositions in base normed spaces
Simplex spaces
Representation of Banach lattices
Order ideals in ordered Banach spaces
Order bounded operators and central measures
Ordered normed tensor products
Positive linear maps of C*-algebras
Axiomatics of preparing and measuring procedures
The structure of ordered Banach spaces in axiomatic quantum mechanics
Measuring and preparing processes
Models of the measuring process and of macro-theories
The centre of a physical system
Operations and effects in the Hilbert space formulation of quantum theory
The empirical logic approach to the physical sciences
The structure of quantum Suggestions for a unified physics
Irreversibility and dynamical maps of statistical operators
The inner orthogonality of convex sets in axiomatic quantum mechanics
Reduced dynamics in quantum mechanics
The quantum mechanical Hilbert space formalism and the quantum mechanical probability space of the outcomes of measurements
Mean ergodic semigroups and invariant ideals in ordered Banach spaces
The representation of classical systems in quantum mechanics
Extended Hilbert space formulation of Dirac's bra and ket formalism and its applications to abstract stationary scattering theory
Projections on orthomodular lattices
The Šilov boundary of a convex cone
A Radon-Nikodym-Theorem for operators with an application to spectral theory