By Erik M. Alfsen
During this e-book we supply an entire 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 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 country areas is not just of curiosity in itself, yet is additionally a major intermediate step in the direction of the characterization of the nation areas of the associative algebras. This ebook offers a whole and up-to-date presentation of the nature ization theorems of '  and . Our prior booklet country areas of operator algebras: simple idea, 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 inspiration of orientations of kingdom areas. For the ease of the reader, we've got summarized those necessities in an appendix which includes all correct 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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