State Spaces of Operator Algebras
Basic Theory, Orientations, and C*-products
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Beschreibung
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.
Autor*in
Erik M. Alfsen
Themen in »State Spaces of Operator Algebras«
algebra applications of mathematics functional analysis geometry mathematical physics operator algebras
Stimmen zu »State Spaces of Operator Algebras«
"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
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