Multilinear Operator Integrals

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.

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

Zusammenfassung

"The present book is a good source for studying multilinear operator integrals and their applications." (Yuri I. Karlovich, zbMATH 1458.47003, 2021)

Inhalt

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