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Non-Associative Normed Algebras 2 Volume Hardback Set (Hardcover)
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Non-Associative Normed Algebras 2 Volume Hardback Set (Hardcover)
Series: Encyclopedia of Mathematics and its Applications
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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unpublished results and is sure to become a central resource for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. The 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 revisits
JB*-triples, covers Zel'manov's celebrated work in Jordan theory,
proves the unit-free variant of the Vidav-Palmer theorem, and
develops the representation theory of alternative C*-algebras and
non-commutative JB*-algebras. 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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