TY  - BOOK
AU  - Skripka,Anna
AU  - Tomskova,Anna
ED  - SpringerLink (Online service)
TI  - Multilinear Operator Integrals: Theory and Applications 
T2  - Lecture Notes in Mathematics,
SN  - 9783030324063
AV  - QA329-329.9 
U1  - 515.724 23
PY  - 2019///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Operator theory
KW  - Functional analysis
KW  - Matrix theory
KW  - Algebra
KW  - Mathematical physics
KW  - Operator Theory
KW  - Functional Analysis
KW  - Linear and Multilinear Algebras, Matrix Theory
KW  - Mathematical Physics
N1  - - Introduction. - Notations and Preliminaries -- Double Operator Integrals -- Multiple Operator Integrals -- Applications
N2  - 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
UR  - https://doi.org/10.1007/978-3-030-32406-3
ER  -