Abstract
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.
Original language | English |
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Place of Publication | Cham, Switzerland |
Publisher | Birkhauser |
Number of pages | 577 |
ISBN (Electronic) | 978-3-031-49654-7 |
ISBN (Print) | 978-3-031-49653-0 |
DOIs | |
Publication status | Published - 2023 |
Publication series
Name | Progress in Mathematics |
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Volume | 349 |
ISSN (Print) | 0743-1643 |
ISSN (Electronic) | 2296-505X |
Bibliographical note
Publisher Copyright:© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.
Keywords
- Banach Spaces
- Noncommutative Analysis
- Noncommutative Integration
- Operator Theory
- von Neumann Algebras