Indeholder "Preface", "Contents of Volume II", "Chapter 1. Linear Spaces", " 1.1 Algebraic results", " 1.2 Linear topological Spaces", " 1.3 Weak topologies", " 1.4 Extreme points", " 1.5 Normed spaces", " 1.6 Linear functionals on normed spaces", " 1.7 Some examples of Banach spaces", " 1.8 Linear operators acting on Banach spaces", " 1.9 Exercises", "Chapter 2. Basics of Hilbert Space and Linear Operators", " 2.1 Inner products on linear spaces", " 2.2 Orthogonality", " 2.3 The weak topology", " 2.4 Linear operators", " General theory", " Classes of operators", " 2.5 The lattice of projections", " 2.6 Constructions with Hilbert spaces", " Subspaces", " Direct sums", " Tensor products and the Hilbert-Schmidt class", " Matrix representations", " 2.7 Unbounded linear operators", " 2.8 Exercises", "Chapter 3. Banach Algebras", " 3.1 Basics", " 3.2 The spectrum", " The Banach algebra L1(R) and Fourier analysis", " 3.3 The Holomorphic Function Calculus", " Holomorphic functions", " The holomorphic function calculus", " 3.4 The Banach algebra C(X)", " 3.5 Exercises", "Chapter 4. Elementary C*-Algebra Theory", " 4.1 Basics", " 4.2 Order structure", " 4.3 Positive linear functionals", " 4.4 Abelian algebras", " 4.5 States and representations", " 4.6 Exercises", "Chapter 5. Elementary von Neumann Algebra Theory", " 5.1 The weak- and strong-operator topologies", " 5.2 Spectral theory for bounded operators", " 5.3 Two fundamental approximation theorems", " 5.4 Irreducible algebras - an application", " 5.5 Projection techniques and constructs", " Central carriers", " Some constructions", " Cyclicity, separation, and countable decomposability", " 5.6 Unbounded operators and abelian von Neumann Algebras", " 5.7 Exercises", "Bibliography", "Index of Notation", "Index".

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