Non-Associative Normed Algebras 2 Volume Hardback Set

Non-Associative Normed Algebras, Volume 2: Representation Theory and the Zel’manov Approach
Contents for Volume 2
Contents for Volume 1
Preface
	The core of the book revisited
	The content of Volume 2
		Chapter 5
		Chapter 6
		Chapter 7
		Chapter 8
	On the historical notes
	Acknowledgements
5 Non-commutative JBW*-algebras, JB*-triples revisited, and a unit-free Vidav–Palmer type non-associative theorem
	5.1 Non-commutative JBW*-algebras
		5.1.1 The results
		5.1.2 Historical notes and comments
	5.2 Preliminaries on analytic mappings
		5.2.1 Polynomials and higher derivatives
		5.2.2 Analytic mappings on Banach spaces
		5.2.3 Holomorphic mappings
		5.2.4 Historical notes and comments
	5.3 Holomorphic automorphisms of a bounded domain
		5.3.1 The topology of the local uniform convergence
		5.3.2 Holomorphic automorphisms of a bounded domain
		5.3.3 The Carathéodory distance on a bounded domain
		5.3.4 Historical notes and comments
	5.4 Complete holomorphic vector fields
		5.4.1 Locally Lipschitz vector fields
		5.4.2 Holomorphic vector fields
		5.4.3 Complete holomorphic vector fields and one-parameter groups
		5.4.4 Historical notes and comments
	5.5 Banach Lie structures for aut(Ω) and Aut(Ω)
		5.5.1 The real Banach Lie algebra aut(Ω)
		5.5.2 The real Banach Lie group Aut(Ω)
		5.5.3 Historical notes and comments
	5.6 Kaup’s holomorphic characterization of JB*-triples
		5.6.1 Bounded circular domains
		5.6.2 The symmetric part of a complex Banach space
		5.6.5 Historical notes and comments
	5.7 JBW*-triples
		5.7.1 The bidual of a JB*-triple
		5.7.2 The main results
		5.7.3 Historical notes and comments
	5.8 Operators into the predual of a JBW*-triple
		5.8.1 On Pełczyński’s property (V*)
		5.8.2 L-embedded spaces have property (V*)
		5.8.3 Applications to JB*-triples
		5.8.4 Historical notes and comments
	5.9 A holomorphic characterization of non-commutative JB*-algebras
		5.9.1 Complete normed algebras whose biduals are non-commutative JB*-algebras
		5.9.2 The main result
		5.9.3 Historical notes and comments
	5.10 Complements on non-commutative JB*-algebras and JB*-triples
		5.10.1 Selected topics in the theory of non-commutative JBW*-algebras
		5.10.2 The strong* topology of a JBW*-triple
		5.10.3 Isometries of non-commutative JB*-algebras
		5.10.4 Historical notes and comments
6 Representation theory for non-commutative JB*-algebras and alternative C*-algebras
	6.1 The main results
		6.1.1 Factor representations of non-commutative JB*-algebras
		6.1.2 Associativity and commutativity of non-commutative JB*-algebras
		6.1.3 JBW*-factors
		6.1.4 Classifying prime JB*-algebras: a Zel’manovian approach
		6.1.5 Prime non-commutative JB*-algebras are centrally closed
		6.1.6 Non-commutative JBW*-factors and alternative W*-factors
		6.1.7 Historical notes and comments
	6.2 Applications of the representation theory
		6.2.1 Alternative C*- and W*-algebras
		6.2.2 The strong topology of a non-commutative JBW*-algebra
		6.2.3 Prime non-commutative JB*-algebras
		6.2.4 Historical notes and comments
	6.3 A further application: commutativity of non-commutative JB*-algebras
		6.3.1 Le Page’s theorem, and some non-associative variants
		6.3.2 The main result
		6.3.3 Discussion of results and methods
		6.3.4 Historical notes and comments
7 Zel’manov approach
	7.1 Classifying prime JB*-triples
		7.1.1 Representation theory for JB*-triples
		7.1.2 Building prime JB*-triples from prime C*-algebras
		7.1.3 The main results
		7.1.4 Historical notes and comments
	7.2 A survey on the analytic treatment of Zel’manov’s prime theorems
		7.2.1 Complete normed J-primitive Jordan algebras
		7.2.2 Strong-versus-light normed versions of the Zel’manov prime theorem
		7.2.3 The norm extension problem
8 Selected topics in the theory of non-associative normed algebras
	8.1 H*-algebras
		8.1.1 Preliminaries, and a theorem on power-associative H*-algebras
		8.1.2 Structure theory
		8.1.3 Topologically simple H*-algebras are ‘very’ prime
		8.1.4 Automatic continuity
		8.1.5 Isomorphisms and derivations of H*-algebras
		8.1.6 Jordan axioms for associative H*-algebras
		8.1.7 Real versus complex H*-algebras
		8.1.8 Trace-class elements in H*-algebras
		8.1.9 Historical notes and comments
	8.2 Extending the theory of H*-algebras: generalized annihilator normed algebras
		8.2.1 The main result
		8.2.2 Generalized annihilator algebras are multiplicatively semiprime
		8.2.3 Generalized complemented normed algebras
		8.2.4 Historical notes and comments
	8.3 Continuing the theory of non-associative normed algebras
		8.3.1 Continuity of homomorphisms into normed algebras without topological divisors of zero
		8.3.2 Complete normed Jordan algebras with finite J-spectrum
		8.3.3 Historical notes and comments
	8.3.4 Normed Jordan algebras after Aupetit’s paper [40]: a survey
	8.4 The joint spectral radius of a bounded set
		8.4.1 Basic notions and results
		8.4.2 Topologically nilpotent normed algebras
		8.4.3 Involving nearly absolute-valued algebras
		8.4.4 Involving tensor products
		8.4.5 Historical notes and comments
Bibliography of Volume 1 (updated)
	Papers
	Books
Additional Bibliography to Volume 2
	Papers
	Books
Symbol index for Volume 1
Subject index for Volume 1
Symbol index for Volume 2
Subject index for Volume 2