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Multilinear Operator Integrals: Theory and Applications 2019 ed. [Minkštas viršelis]

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  • Formatas: Paperback / softback, 192 pages, aukštis x plotis: 235x155 mm, weight: 454 g, 15 Illustrations, black and white; XI, 192 p. 15 illus., 1 Paperback / softback
  • Serija: Lecture Notes in Mathematics 2250
  • Išleidimo metai: 02-Dec-2019
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030324052
  • ISBN-13: 9783030324056
Kitos knygos pagal šią temą:
Multilinear Operator Integrals: Theory and Applications 2019 ed.Didesnis paveikslėlis
  • Formatas: Paperback / softback, 192 pages, aukštis x plotis: 235x155 mm, weight: 454 g, 15 Illustrations, black and white; XI, 192 p. 15 illus., 1 Paperback / softback
  • Serija: Lecture Notes in Mathematics 2250
  • Išleidimo metai: 02-Dec-2019
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030324052
  • ISBN-13: 9783030324056
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783030324056.html
Raktažodžiai:

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.

Recenzijos

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

1 Introduction
1(6)
2 Notations and Preliminaries
7(28)
2.1 Spaces of Functions
7(3)
2.2 Divided Differences
10(1)
2.3 Linear Operators
11(1)
2.4 Schatten-von Neumann Classes
12(3)
2.5 Product of Spectral Measures
15(3)
2.6 Classical Noncommutative Lp-Spaces and Weak Lp-Spaces
18(4)
2.7 The Haagerup Lp-Space
22(2)
2.8 Symmetrically Normed Ideals
24(2)
2.9 Traces on L1-∞ (M, τ)
26(3)
2.10 Banach Spaces and Spectral Operators
29(3)
2.11 Differentiability of Maps on Banach Spaces
32(3)
3 Double Operator Integrals
35(30)
3.1 Double Operator Integrals on Finite Matrices
35(6)
3.1.1 Definition
36(1)
3.1.2 Relation to Finite-Dimensional Schur Multipliers
36(1)
3.1.3 Properties of Finite Dimensional Double Operator Integrals
37(4)
3.2 Double Operator Integrals on S2
41(4)
3.2.1 Definition
41(2)
3.2.2 Relation to Schur Multipliers on S2
43(1)
3.2.3 Basic Properties of Double Operator Integrals on S2
44(1)
3.3 Double Operator Integrals on Schatten Classes and SCH)
45(15)
3.3.1 Daletskii-Krein's Approach
45(1)
3.3.2 Extension from the Double Operator Integral on S2
46(1)
3.3.3 Approach via Separation of Variables
47(3)
3.3.4 Approach Without Separation of Variables
50(1)
3.3.5 Properties of Double Operator Integrals on Sp and B(H)
51(3)
3.3.6 Symbols of Bounded Double Operator Integrals
54(4)
3.3.7 Transference Principle
58(2)
3.4 Nonself-adjointCase
60(1)
3.5 Double Operator Integrals on Noncommutative Lp-Spaces
60(3)
3.5.1 Extension from the Double Operator Integral on L2(M, τ)
61(1)
3.5.2 Approach via Separation of Variables
61(1)
3.5.3 Approach Without Separation of Variables
61(1)
3.5.4 Properties of Double Operator Integrals on Lp'(M, τ)
62(1)
3.6 Double Operator Integrals on Banach Spaces
63(2)
4 Multiple Operator Integrals
65(48)
4.1 Multiple Operator Integrals on Finite Matrices
65(9)
4.1.1 Definition
65(1)
4.1.2 Relation to Multilinear Schur Multipliers
66(1)
4.1.3 Properties of Finite Dimensional Multiple Operator Integrals
67(7)
4.1.4 Estimates of Multiple Operator Integrals via Double Operator Integrals
74(1)
4.2 Multiple Operator Integrals on S2
74(3)
4.2.1 Pavlov's Approach
74(1)
4.2.2 Coine-Le Merdy-Sukochev's Approach
75(2)
4.3 Multiple Operator Integrals on Schatten Classes and 23(7f)
77(23)
4.3.1 Approach via Separation of Variables
77(2)
4.3.2 Approach Without Separation of Variables
79(2)
4.3.3 Properties of Multiple Operator Integrals on Sp and B(H)
81(12)
4.3.4 Nonself-adjoint Case
93(6)
4.3.5 Change of Variables
99(1)
4.4 Multiple Operator Integrals on Noncommutative and Weak Lp-Spaces
100(13)
4.4.1 Approach via Separation of Variables
100(1)
4.4.2 Approach Without Separation of Variables
100(1)
4.4.3 Properties of Multiple Operator Integrals on Lp,∞(M, τ)
101(12)
5 Applications
113(66)
5.1 Operator Lipschitz Functions
113(15)
5.1.1 Commutator and Lipschitz Estimates in S2
114(1)
5.1.2 Commutator and Lipschitz Estimates in Sp and B(H)
115(4)
5.1.3 Commutator and Lipschitz Estimates: Nonself-adjoint Case
119(2)
5.1.4 Lipschitz Type Estimates in Noncommutative Lp-Spaces
121(1)
5.1.5 Lipschitz Type Estimates in Banach Spaces
122(1)
5.1.6 Operator I-Lipschitz Functions
123(5)
5.2 Operator Holder Functions
128(1)
5.3 Differentiation of Operator Functions
129(16)
5.3.1 Differentiation of Matrix Functions
129(3)
5.3.2 Differentiation in Along Multiplicative Paths of Unitaries
132(3)
5.3.3 Differentiation in B(H) and S1 Along Linear Paths of Self-adjoints
135(2)
5.3.4 Differentiation in Sp Along Linear Paths of Self-adjoints
137(3)
5.3.5 Differentiation of Functions of Contractive and Dissipative Operators
140(1)
5.3.6 Differentiation in Noncommutative Lp-Spaces
141(1)
5.3.7 Gateaux and Frechet I-Differentiable Functions
142(3)
5.4 Taylor Approximation of Operator Functions
145(9)
5.4.1 Taylor Remainders of Matrix Functions
145(4)
5.4.2 Taylor Remainders for Perturbations in Sp and B(H)
149(4)
5.4.3 Taylor Remainders for Unsummable Perturbations
153(1)
5.5 Spectral Shift
154(12)
5.5.1 Spectral Shift Function for Self-adjoint Operators
155(7)
5.5.2 Spectral Shift Function for Nonself-adjoint Operators
162(3)
5.5.3 Spectral Shift Measure in the Setting of von Neumann Algebras
165(1)
5.6 Spectral Flow
166(4)
5.7 Quantum Differentiability
170(2)
5.8 Differentiation of Noncommutative Lp-Norms
172(7)
References 179(10)
Index 189