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Multilinear Operator Integrals

Theory and Applications

  • Anna Skripka
  • Anna Tomskova
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2250)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Anna Skripka, Anna Tomskova
    Pages 1-5
  3. Anna Skripka, Anna Tomskova
    Pages 7-34
  4. Anna Skripka, Anna Tomskova
    Pages 35-64
  5. Anna Skripka, Anna Tomskova
    Pages 65-112
  6. Anna Skripka, Anna Tomskova
    Pages 113-177
  7. Back Matter
    Pages 179-192

About this book

Introduction

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.

Keywords

Fréchet Derivative Gâteaux Multilinear Schur Multiplier Multiple Operator Integral Noncommutative Lp Space Operator Hölder Function Operator Lipschitz Quantized Derivative Spectral Flow Spectral Shift Function Symmetrically Normed Ideal Trace Formula

Authors and affiliations

  • Anna Skripka
    • 1
  • Anna Tomskova
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA
  2. 2.School of Computer Science and EngineeringInha University in TashkentTashkentUzbekistan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-32406-3
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-32405-6
  • Online ISBN 978-3-030-32406-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site