Lectures on selected topics in von Neumann algebras
By: Fumio Hiai
Series: EMS series of lectures in mathematics; EMS series of lectures in mathematics
Publisher: EMS Press
Published: 2021
Place of publication: Berlin, Germany
Language: eng
Number of pages: 241
ISBN-13: 9783985470044
Copyright date: 2021
Subjects: Von Neumann algebras
Description: "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."- publisher
Notes: Includes bibliographical references (pages 231-237) and index.
Table of contents: title: Von Neumann algebras, an overview; title: Tomita-Takesaki modular theory; title: Standard form; title: [tau]-Measurable operators; title: Conditional expectations and generalized conditional expectations; title: Connes' cocycle derivatives; title: Operator-valued weights; title: Takesaki duality and structure theory; title: Haagerup's Lp-spaces; title: Relative modular operators and Connes' cocycle derivaties (continued); title: Spatial derivatives and spatial Lp-spaces.