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The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.
List of contents
- 1. A Review of Relevant Operator Theory. - 2. Measurable Operators. - 3. Singular Value Functions. - 4. Symmetric Spaces of -Measurable Operators. - 5. Strongly Symmetric Spaces of -Measurable Operators. - 6. Examples. - 7. Interpolation.
About the author
Peter Dodds is Emeritus Professor of Mathematics at Flinders University, Tonsley, Australia.
Ben de Pagter is Emeritus Professor of Mathematics at Delft University of Technology, Delft, The Netherlands.
Fedor Sukochev is Professor of Mathematics at the University of New South Wales, Sydney, Australia.
Report
"The book will serve best those who want to familiarise themselves with this beautiful theory, but will be useful to both graduate students and researchers interested in noncommutative measure and integration theory. ... It is written very clearly and the exposition is thoroughly modern, enabling uniform treatments of subjects ... . It should serve the mathematical community well in the years to come." (Stanislaw Goldstein, zbMATH 1545.46002, 2024)
