Download E-books Geometry of State Spaces of Operator Algebras (Mathematics: Theory & Applications) PDF

By Erik M. Alfsen

During this publication we supply 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 nation 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 is additionally an incredible intermediate step in the direction of the characterization of the country areas of the associative algebras. This booklet offers an entire and up to date presentation of the nature­ ization theorems of [10]' [11] and [71]. Our past ebook nation areas of operator algebras: uncomplicated idea, orientations and C*-products, referenced as [AS] within the sequel, supplies an account of the required necessities on C*-algebras and von Neumann algebras, in addition to a dialogue of the most important idea of orientations of nation areas. For the benefit of the reader, we've got summarized those must haves in an appendix which includes all appropriate definitions and effects (listed as (AI), (A2), ... ), in regards again to [AS] for proofs, in order that this publication is self-contained.

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