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AuthorAlfsen, Erik M. author
TitleGeometry of State Spaces of Operator Algebras [electronic resource] / by Erik M. Alfsen, Frederic W. Shultz
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4612-0019-2
Descript XIII, 467 p. online resource

SUMMARY

In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These nonยญ associative algebras generalize C*-algebras and von Neumann algebras reยญ spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the characterยญ ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained


CONTENT

I: Jordan Algebras and Their State Spaces -- 1: JB-algebras -- 2: JBW-algebras -- 3: Structure of JBW-algebras -- 4: Representations of JB-algebras -- 5: State Spaces of Jordan Algebras -- 6: Dynamical Correspondences -- II: Convexity and Spectral Theory -- 7: General Compressions -- 8: Spectral Theory -- III: State Space Characterizations -- 9: Characterization of Jordan Algebra State Spaces -- 10: Characterization of Normal State Spaces of von Neumann Algebras -- 11: Characterization of C*-algebra State Spaces


Mathematics Algebra Operator theory Applied mathematics Engineering mathematics Physics Mathematics Algebra Operator Theory Applications of Mathematics Theoretical Mathematical and Computational Physics



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