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Lectures on Selected Topics in von Neumann Algebras
EMS Series of Lectures in Mathematics

Fumio Hiai (Tohoku University, Japan)

Lectures on Selected Topics in von Neumann Algebras

ISBN print 978-3-98547-004-4, ISBN online 978-3-98547-504-9
DOI 10.4171/ELM/32
April 2021, 250 pages, softcover, 17 x 24 cm.
39.00 Euro

The theory of von Neumann algebras, originating with the work of F. J. Murray and J. von Neumann in the late 1930s, has grown into a rich discipline with connections to different branches of mathematics and physics. Following the breakthrough of Tomita–Takesaki theory, many great advances were made throughout the 1970s by H. Araki, A. Connes, U. Haagerup, M. Takesaki and others.

These lecture notes aim to present a fast-track study of some important topics in classical parts of von Neumann algebra theory that were developed in the 1970s. Starting with Tomita–Takesaki theory, this book covers topics such as the standard form, Connes’ cocycle derivatives, operator-valued weights, type III structure theory and non-commutative integration theory.

The self-contained presentation of the material makes this book useful not only to graduate students and researchers who want to know the fundamentals of von Neumann algebras, but also to interested undergraduates who have a basic knowledge of functional analysis and measure theory.

Keywords: von Neumann algebra, Tomita–Takesaki theory, modular operator, standard form, Connes’ cocycle derivative, operator-valued weight, relative modular operator, crossed product, KMS condition, Takesaki’s duality theorem,