Multilinear Operator Integrals

Theory and Applications
1. Auflage 2019
ISBN: 978-3-030-32405-6
Verlag: Springer International Publishing

Buch, Englisch, Band 2250, 192 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 318 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Tomskova, Anna

Skripka, Anna

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

- Introduction. - Notations and Preliminaries.- Double Operator Integrals.- Multiple Operator Integrals.- Applications.