Noncommutative Integration and Operator Theory

Peter G. Dodds, Ben de Pagter, Fedor A. Sukochev (Autoren)

Buch | Softcover

XI, 577 Seiten

2025
Springer International Publishing (Verlag)
9783031496561 (ISBN)

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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.

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.

- 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.

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. (Stanislaw Goldstein, zbMATH 1545.46002, 2024)

Erscheinungsdatum	20.01.2025
Reihe/Serie	Progress in Mathematics
Zusatzinfo	XI, 577 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Banach spaces • noncommutative analysis • Noncommutative Integration • operator theory • von neumann algebras
ISBN-13	9783031496561 / 9783031496561
Zustand	Neuware