State Spaces of Operator Algebras : Basic Theory, Orientations, and C*-products

Alfsen, Erik M.; Shultz, Frederik W.

ISBN 10: 1461266343 / ISBN 13: 9781461266341

Editore: Birkhäuser, 2012

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Dati bibliografici

• Titolo: State Spaces of Operator Algebras : Basic Theory, Orientations, and C*-products
• Editore: Birkhäuser
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461266343
• ISBN 13: 9781461266341
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

Self-contained work, focusing on the theory of state spaces of C*- algebras and von Neumann algebras. Gives a new presentation of the theory of orientation of state spaces of C*-algebras that does not depend on Jordan algebras. Also presented is the theory of orientation of normal state spaces of von Neumann algebras, with complete proofs for the first time. Minimal prerequisites: knowledge from standard graduate courses in real and complex variables, measure theory, and functional analysis. Intended for specialists in operator algebras, as well as graduate students and mathematicians seeking an overview of the field.

Recensione

"This excellent book was born out of the authors’ successful attempts to answer questions [like] ‘When is a compact convex set the state space of a C*-algebra?’ . . . I would regard the book as essential reading for any graduate student working in C*-algebras and related areas, particularly those with an interest in geometry."

―Zentralblatt Math

"A useful introduction to an elegant aspect of the theory of operator algebras which has close links to mathematical physics, as well as being of interest in its own right."

―Mathematical Reviews

"This self-contained work, focusing on the theory of state spaces of C*-algebras and von Neumann algebras, explains how the oriented state space geometrically determines the algebra...The theory of operator algebras was initially motivated by applications to physics, but has recently found unexpected new applications to fields of pure mathematics as diverse as foliations and knot theory." ---Analele Stiintifice ale Universitatii,,al. I. Cuza din Iasi