Noncommutative Integration and Operator Theory
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Beschreibung
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.
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.
Connects to previous approaches and relates to classical works in the field Core exploration of noncommutative integration, both for students and for expert mathematicians Overview on the theory of operator ideals and of rearrangement invariant Banach lattices of measurable functions
Autor*in
Peter G. Dodds
Themen in »Noncommutative Integration and Operator Theory«
Noncommutative Integration Operator Theory Banach Spaces von Neumann Algebras Noncommutative Analysis
Stimmen zu »Noncommutative Integration and Operator Theory«
“This book is a masterful work that synthesizes classical Banach space theory and operator theory within the noncommutative framework, offering reworked proofs and new insights. The text is a valuable resource for researchers and students aiming to explore the deep interplay between analysis, geometry, and operator algebras. Its detailed expositions and examples make it an essential reference for advancing in noncommutative integration and operator theory.” (Xudong Lai, Mathematical Reviews, June, 2025)
“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.” (Stanisław Goldstein, zbMATH 1545.46002, 2024)
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