General Theory of C*-Algebras

Introduction.

4. C*-Algebras.

4.1 The General Theory.

4.1.1 General Results.

4.1.2 The Symmetry of C*-algebra.

4.1.3 Functional calculus in C*-algebras.

4.1.4 The Theorem of Fuglede-Putnam

4.2 The Order Relation

4.2.1 Definition and General Properties

4.2.2 More about the Order Relation

4.2.3 Examples

4.2.4 Powers of Positive Elements

4.2.5 The Modulus

4.2.6 Ideals and Quotients of C*-algebras.

4.2.7 The Ordered Set of Orthogonal Projections.

4.2.8 Approximate Unit.

4.3 Supplementary Results on C*-algebras.

4.3.1 The Exterior Multiplication.

4.3.2 Order Complete C*-algebras.

4.3.3 The Carrier.

4.3.4 Hereditary C*-Subalgebras.

4.3.5 Simple C*-algebras.

4.3.6 Supplementary Results Concerning Complexification.

4.4 W*-algebras.

4.4.1 General Properties.

4.4.2 F as an E-submodule of E¹.

4.4.3 Polar Representation.

4.4.4 W*-Homomorphisms.

Name Index. Subject Index. Symbol Index.