Geometry of State Spaces of Operator Algebras (Mathematics: by Erik M. Alfsen,Frederic W. Shultz

By Erik M. Alfsen,Frederic W. Shultz

during this ebook we provide a whole geometric description of nation areas of operator algebras, Jordan in addition to associative. that's, we provide axiomatic characterizations of these convex units which are kingdom areas of C*-algebras and von Neumann algebras, including such characterizations for the normed Jordan algebras referred to as JB-algebras and JBW-algebras. those non­ associative algebras generalize C*-algebras and von Neumann algebras re­ spectively, and the characterization in their country areas is not just of curiosity in itself, yet can be a big intermediate step in the direction of the characterization of the country areas of the associative algebras. This e-book provides a whole and up to date presentation of the nature­ ization theorems of [10]' [11] and [71]. Our earlier e-book nation areas of operator algebras: easy conception, orientations and C*-products, referenced as [AS] within the sequel, supplies an account of the mandatory necessities on C*-algebras and von Neumann algebras, in addition to a dialogue of the most important concept of orientations of kingdom areas. For the benefit of the reader, we now have summarized those necessities in an appendix which includes all suitable definitions and effects (listed as (AI), (A2), ... ), in regards again to [AS] for proofs, in order that this booklet is self-contained.

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