ENGLISH

Multilinear Operator Integrals: Theory and Applications

By Anna Skripka , Anna Tomskova

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-32405-6, 978-3-030-32406-3
Language
english
Format
PDF
Filesize
2 MB (2453484 bytes)
Series
Lecture Notes in Mathematics 2250
Edition
1st ed. 2019
Pages
XI, 192\200
Time added
2020-02-08 04:41:59
Mathematics; Operator Theory; Functional Analysis;Matrix Theory; Mathematical Physics

Description

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. Front Matter ....Pages i-xi Introduction (Anna Skripka, Anna Tomskova)....Pages 1-5 Notations and Preliminaries (Anna Skripka, Anna Tomskova)....Pages 7-34 Double Operator Integrals (Anna Skripka, Anna Tomskova)....Pages 35-64 Multiple Operator Integrals (Anna Skripka, Anna Tomskova)....Pages 65-112 Applications (Anna Skripka, Anna Tomskova)....Pages 113-177 Back Matter ....Pages 179-192

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