Multilinear Operator Integrals

Theory and Applications

Anna Skripka, Anna Tomskova (Autoren)

Buch | Softcover

XI, 192 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-32405-6 (ISBN)

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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.

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

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

Erscheinungsdatum	03.12.2019
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XI, 192 p. 15 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	320 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Fréchet derivative • gâteaux • matrix theory • 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
ISBN-10	3-030-32405-2 / 3030324052
ISBN-13	978-3-030-32405-6 / 9783030324056
Zustand	Neuware