Lectures on C∗-Algebras (Math 582)

Lecture 1 Introduction
Lecture 2 Hilbert space
Lecture 3 Fredholm theory
Lecture 4 Banach algebras
Lecture 5 C*-algebra basics and the Gelfand-Naimark theorem
Lecture 6 Functional calculus and positivity
Lecture 7 Positivity and order
Lecture 8 Ideals and quotients
Lecture 9 Examples of C*-algebras
Lecture 10 Hilbert modules and multipliers
Lecture 11 Review of locally convex spaces
Lecture 12 Topologies on B(H)
Lecture 13 Von Neumann Algebras
Lecture 14 Von Neumann Algebras, representations, and states
Lecture 15 The GNS Construction
Lecture 16 Abelian von Neumann algebras and the spectral theorem
Lecture 17 Pure States and Irreducible Representations
Lecture 18 Around Fell's theorem
Lecture 19 Representations by compact operators
Lecture 20 The Toeplitz algebra and its representations
Lecture 21 The Cuntz Algebras
Lecture 22 Basics on Group C*-Algebras and Harmonic Analysis
Lecture 23 Some More Harmonic Analysis
Lecture 24 Amenability I
Lecture 25 Amenability II
Lecture 26 Free Group C*-Algebras
Lecture 27 Free Group C*-Algebras II
Lecture 28 Completely Positive Maps and Nuclearity I
Lecture 29 Completely Positive Maps and Nuclearity II
Lecture 30 Nuclearity and Group Algebras
Lecture 31 Approximate Equivalence and the Weyl-von Neumann Theorem
Lecture 32 Brown-Douglas-Fillmore Theory
Lecture 33 More about BDF Theory
Lecture 34 UHF Algebras
Lecture 35 UHF Algebras and von Neumann Factors
Lecture 36 The Classification of Factors
Lecture 37 Weak containment: loose ends