Author | Alfsen, Erik M. author |
---|---|
Title | State Spaces of Operator Algebras [electronic resource] : Basic Theory, Orientations, and C*-products / by Erik M. Alfsen, Frederic W. Shultz |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0147-2 |
Descript | XII, 350 p. online resource |
Preface -- 1: Introduction -- Basic notions from convexity and ordered vector spaces -- Order unit and base norm spaces -- Selected topics in functional analysis -- Spectral theory for monotone complete CR(X) -- Elementary dimension theory in lattices -- Ordered algebras -- Algebras with involution -- Order derivations -- Notes -- 2: Elementary Theory of C*-algebras and von Neumann Algebras -- Basics on C*-algebras -- Representations of C*-algebras -- Preliminaries on $$ \mathcal{B}$$ (H) -- Basics on von Neumann algebras -- Miscellaneous -- Notes -- 3: Ideals, Faces and Compressions -- Projections, ideals, and faces for von Neumann algebras -- Projections, ideals and faces for C*-algebras -- Invariant subspaces -- Compressions of von Neumann algebras -- Notes -- 4: The Normal State Space of 13(H) -- Facial Structure -- The concepts of angle and geodesic metric -- *-isomorphisms and *-anti-isomorphisms -- Orientation of balls and multiplication in M2(C) -- Notes -- 5: States, Representations, and Orientations of C*-algebras -- State space geometry and representations -- The spectrum and primitive ideal space -- Completely positive maps -- Orientations of state spaces -- Orientations and C* structures -- Orientations and non-unital C*-algebras -- Notes -- 6: Symmetries and Rotations in von Neumann Algebras -- Elements of structure theory -- Symmetries and reflections -- Rotational Derivations -- Notes -- 7: Orientations and von Neumann Algebras -- Balanced symmetries and associative products -- Cartesian triples and 3-frames -- Orientation of normal state spaces -- From orientations to associative products -- Notes