Ebook: State Spaces of Operator Algebras: Basic Theory, Orientations, and C*-products
- Tags: Operator Theory, Algebra, Applications of Mathematics, Theoretical Mathematical and Computational Physics
- Series: Mathematics: Theory & Applications
- Year: 2001
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-62
Elementary Theory of C*-algebras and von Neumann Algebras....Pages 63-129
Ideals, Faces and Compressions....Pages 130-175
The Normal State Space of ? (H) ....Pages 176-198
States, Representations, and Orientations of C*-algebras....Pages 199-240
Symmetries and Rotations in von Neumann Algebras....Pages 241-280
Orientations and von Neumann algebras....Pages 281-340
Back Matter....Pages 341-350
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-62
Elementary Theory of C*-algebras and von Neumann Algebras....Pages 63-129
Ideals, Faces and Compressions....Pages 130-175
The Normal State Space of ? (H) ....Pages 176-198
States, Representations, and Orientations of C*-algebras....Pages 199-240
Symmetries and Rotations in von Neumann Algebras....Pages 241-280
Orientations and von Neumann algebras....Pages 281-340
Back Matter....Pages 341-350
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