By Erik M. Alfsen
During this ebook 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 country areas of C*-algebras and von Neumann algebras, including such characterizations for the normed Jordan algebras known as JB-algebras and JBW-algebras. those non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization in their kingdom areas is not just of curiosity in itself, yet can also be an immense intermediate step in the direction of the characterization of the nation areas of the associative algebras. This e-book provides an entire and up to date presentation of the nature ization theorems of '  and . Our past booklet kingdom areas of operator algebras: easy concept, orientations and C*-products, referenced as [AS] within the sequel, supplies an account of the required must haves on C*-algebras and von Neumann algebras, in addition to a dialogue of the most important idea of orientations of nation areas. For the ease of the reader, we've got 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 e-book is self-contained.
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