This first systematic account of the basic theory of normed
algebras, without assuming associativity, includes many new and
unpublished results and is sure to become a central resource for
researchers and graduate students in the field. This first volume
focuses on the non-associative generalizations of (associative)
C*-algebras provided by the so-called non-associative Gelfand
Naimark and Vidav Palmer theorems, which give rise to alternative
C*-algebras and non-commutative JB*-algebras, respectively. The
relationship between non-commutative JB*-algebras and JB*-triples
is also fully discussed. The second volume covers Zel'manov's
celebrated work in Jordan theory to derive classification theorems
for non-commutative JB*-algebras and JB*-triples, as well as other
topics. The book interweaves pure algebra, geometry of normed
spaces, and complex analysis, and includes a wealth of historical
comments, background material, examples and exercises. The authors
also provide an extensive bibliography."
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