B. V. Bhat

Lectures on operator theory

C*-algebras: C*-algebras: Definitions and examples C*-algebras: Constructions Positivity in C*-algebras K-theory I Tensor products of C*-algebras Crossed products I Crossed products II: Examples Free products K-theory II: Roots in topology and index theory C*-algebraic K-theory made concrete, or trick or treat with

K-theory I

2 \times 2

C*-algebras: Constructions

matrix algebras Dilation theory C*-algebras and mathematical physics C*-algebras and several complex variables von Neumann algebras: Basic structure of von Neumann algebras von Neumann algebras (Type

The range of the invariant

II_1

Relations to minimal models and subfactors

factors) The equivalence between injectivity and hyperfiniteness, part I The equivalence between injectivity and hyperfiniteness, part II On the Jones index Introductory topics on subfactors The Tomita-Takesaki theory explained Free products of von Neumann algebras Semigroups of endomorphisms of

C*-algebraic K-theory made concrete, or trick or treat with 2×2 matrix algebras

\mathcal{B}(H)

Simple AI-algebras and the range of the invariant

Classification of C*-algebras AF-algebras and Bratteli diagrams Classification of amenable C*-algebras I Classification of amenable C*-algebras II Simple AI-algebras and the range of the invariant Classification of simple purely infinite C*-algebras I Hereditary subalgebras of certain simple non real rank zero C*-algebras: Preface Introduction The isomorphism theorem The range of the invariant Bibliography Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors: Preface/Acknowledgements The Kauffman-Lins recoupling theory Graphs and connections An extension of the recoupling model Relations to minimal models and subfactors Bibliography.