Authors:
- Offers a comprehensive, structured treatment of the theory in both finite-dimensional and infinite-dimensional settings
- Includes numerous applications of multilinear operator integral techniques, of interest to a broad audience
- This is the first book of its kind in terms of its subject, scope and style of exposition
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2250)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
This book provides a comprehensive treatment of multilinear operator integral techniques. The exposition is structured to be suitable for a course on methods and applications of multilinear operator integrals and also as a research aid. The ideas and contributions to the field are surveyed and up-to-date results and methods are presented. Most practical constructions of multiple operator integrals are included along with fundamental technical results and major applications to smoothness properties of operator functions (Lipschitz and Hölder continuity, differentiability), approximation of operator functions, spectral shift functions, spectral flow in the setting of noncommutative geometry, quantum differentiability, and differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more involved, technical proofs are outlined and supplemented with references. Selected open problems in the field are also presented.
Reviews
“The present book is a good source for studying multilinear operator integrals and their applications.” (Yuri I. Karlovich, zbMATH 1458.47003, 2021)
Authors and Affiliations
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Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA
Anna Skripka
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School of Computer Science and Engineering, Inha University in Tashkent, Tashkent, Uzbekistan
Anna Tomskova
Bibliographic Information
Book Title: Multilinear Operator Integrals
Book Subtitle: Theory and Applications
Authors: Anna Skripka, Anna Tomskova
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-32406-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-32405-6Published: 02 December 2019
eBook ISBN: 978-3-030-32406-3Published: 01 December 2019
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XI, 192
Number of Illustrations: 15 b/w illustrations
Topics: Operator Theory, Functional Analysis, Linear and Multilinear Algebras, Matrix Theory, Mathematical Physics