Multilinear operator integrals: theory and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2019]
|
| Schriftenreihe: | Lecture notes in mathematics
2250 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | xi, 190 Seiten |
| ISBN: | 9783030324056 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV046322831 | ||
| 003 | DE-604 | ||
| 005 | 20200115 | ||
| 007 | t| | ||
| 008 | 200108s2019 xx |||| 00||| eng d | ||
| 020 | |a 9783030324056 |9 978-3-030-32405-6 | ||
| 035 | |a (OCoLC)1134789417 | ||
| 035 | |a (DE-599)HBZHT020318728 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-824 |a DE-188 | ||
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a 47B49 |2 msc | ||
| 084 | |a 46L51 |2 msc | ||
| 100 | 1 | |a Skripka, Anna |0 (DE-588)1202019110 |4 aut | |
| 245 | 1 | 0 | |a Multilinear operator integrals |b theory and applications |c Anna Skripka, Anna Tomskova |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2019] | |
| 300 | |a xi, 190 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2250 | |
| 650 | 0 | 7 | |a Integraloperator |0 (DE-588)4131247-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Multilineare Abbildung |0 (DE-588)4479794-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Operatortheorie |0 (DE-588)4075665-8 |D s |
| 689 | 0 | 1 | |a Integraloperator |0 (DE-588)4131247-8 |D s |
| 689 | 0 | 2 | |a Multilineare Abbildung |0 (DE-588)4479794-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tomskova, Anna |d ca. 20./21. Jahrhundert |0 (DE-588)1202614329 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-030-32406-3 |
| 830 | 0 | |a Lecture notes in mathematics |v 2250 |w (DE-604)BV000676446 |9 2250 | |
| 856 | 4 | 2 | |m V:DE-605;X:semantics |q application/pdf |u http://digitale-objekte.hbz-nrw.de/storage2/2019/12/22/file_27/8797916.pdf |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031699816&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-031699816 | |
Datensatz im Suchindex
| _version_ | 1822792262672711680 |
|---|---|
| adam_text |
Anna Skripka • Anna Tomskova
Multilinear Operator
Integrals
Theory and Applications
Ö Springer
Anna Skripka Anna Tomskova
Department of Mathematics and Statistics School of Computer Science and
University of New Mexico Engineering
Albuquerque, NM, USA Inha University in Tashkent
Tashkent, Uzbekistan
ISSN 0075-8434 ISSN 1617-9692 (electronic)
Lecture Notes in Mathematics
ISBN 978-3-030-32405-6 ISBN 978-3-030-32406-3 (eBook)
https://doi org/10 1007/978-3-030-32406-3
Mathematics Subject Classification (2010): Primary: 46L51, 47B49 47A60, 47A63, 47B10, 47C15,
47A55, 15A60; Secondary: 46N50,58J30,46L87,46GI2,46H10,471-25, 26A16
© Springer Nature Switzerland AG 2019
This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed
The use of general descriptive names, registered names, trademarks, service marks, etc in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbeslrasse 11,6330 Cham, Switzerland
Preface
A multilinear operator integral is a powerful tool in noncommutative analysis
and its applications Theory underlying multilinear operator integration has been
developing since the 1950s, with a number of amazing advancements made in
recent years The field has accumulated many deep theoretical results and important
applications, but no book on this beautiful and important subject appeared in the
literature This book provides a brief yet comprehensive treatment of multilinear
operator integral techniques and their applications, partially filling the gap in the
literature The exposition is structured to be suitable for both a topics course and a
research aid on methods, results, and applications of multilinear operator integrals
We survey on earlier ideas and contributions to the field and then present in
greater detail the best up-to-date results and modem methods The content includes
most practical, refined constructions of multiple operator integrals and fundamental
technical results along with major applications of this tool to smoothness properties
of operator functions (Lipschitz continuity, Holder continuity, differentiability),
approximation of operator functions, spectral shift functions, spectral flow in the
setting of noncommutative geometry, quantum differentiability, and differentiability
of noncommutative Lp norms We demonstrate ideas and include proofs in simpler
cases, while highly technical proofs are outlined and supplemented with a list of
references We also state selected open problems in the field
Albuquerque, NM, USA
Tashkent, Uzbekistan
September 2019
Anna Skripka
Anna Tomskova
Contents
1 Introduction 1
2 Notations and Preliminaries 7
2 1 Spaces of Functions 7
2 2 Divided Differences 10
2 3 Linear Operators 11
2 4 Schatten-von Neumann Classes 12
2 5 Product of Spectral Measures 15
2 6 Classical Noncommutative Lp-Spaces and Weak Lp-Spaces 18
2 7 The Haagerup Lp-Space 22
2 8 Symmetrically Normed Ideals 24
2 9 Traces on Li oo(M, r) 26
2 10 Banach Spaces and Spectral Operators 29
2 11 Differentiability of Maps on Banach Spaces 32
3 Double Operator Integrals 35
3 1 Double Operator Integrals on Finite Matrices 35
311 Definition 36
312 Relation to Finite-Dimensional Schur Multipliers 36
313 Properties of Finite Dimensional Double Operator
Integrals 37
3 2 Double Operator Integrals on 52 41
321 Definition 41
322 Relation to Schur Multipliers on S2 43
323 Basic Properties of Double Operator Integrals on S2 44
3 3 Double Operator Integrals on Schatten Classes and SfH) 45
331 Daletskii-Krein’s Approach 45
332 Extension from the Double Operator Integral on S2 46
333 Approach via Separation of Variables 47
334 Approach Without Separation of Variables 50
335 Properties of Double Operator Integrals on Sp
andS('H) 51
ix
Contents
336 Symbols of Bounded Double Operator Integrals 54
337 Transference Principle 58
3 4 Nonself-adjoint Case 60
3 5 Double Operator Integrals on Noncommutative Lp-Spaces 60
351 Extension from the Double Operator Integral
on L2(M, t) 61
352 Approach via Separation of Variables 61
353 Approach Without Separation of Variables 61
354 Properties of Double Operator Integrals on LP(M, r) 62
3 6 Double Operator Integrals on Banach Spaces 63
4 Multiple Operator Integrals 65
4 1 Multiple Operator Integrals on Finite Matrices 65
411 Definition 65
412 Relation to Multilinear Schur Multipliers 66
413 Properties of Finite Dimensional Multiple Operator
Integrals 67
414 Estimates of Multiple Operator Integrals via Double
Operator Integrals 74
4 2 Multiple Operator Integrals on 52 74
421 Pavlov’s Approach 74
422 Coine-Le Merdy-Sukochev’s Approach 75
4 3 Multiple Operator Integrals on Schatten Classes and SfK) 77
431 Approach via Separation of Variables 77
432 Approach Without Separation of Variables 79
433 Properties of Multiple Operator Integrals on Sp
and SOW) 81
434 Nonself-adjoint Case 93
435 Change of Variables 99
4 4 Multiple Operator Integrals on Noncommutative and Weak
Lp-Spaces 100
441 Approach via Separation of Variables 100
442 Approach Without Separation of Variables 100
443 Properties of Multiple Operator Integrals
on LP-°°(M, r) 101
5 Applications 113
5 1 Operator Lipschitz Functions 113
511 Commutator and Lipschitz Estimates in S2 114
512 Commutator and Lipschitz Estimates in Sp and Si'H) 115
513 Commutator and Lipschitz Estimates: Nonself-adjoint
Case 119
514 Lipschitz Type Estimates in Noncommutative
Lp-Spaces 121
515 Lipschitz Type Estimates in Banach Spaces 122
516 Operator J-Lipschitz Functions 123
Contents xi
5 2 Operator Holder Functions 128
5 3 Differentiation of Operator Functions 129
531 Differentiation of Matrix Functions 129
532 Differentiation in 'ß('H) Along Multiplicative Paths
ofUnitaries 132
533 Differentiation in B('H) and 51 Along Linear Paths
of Self-adjoints 135
534 Differentiation in Sp Along Linear Paths
of Self-adjoints 137
535 Differentiation of Functions of Contractive and
Dissipative Operators 140
536 Differentiation in Noncommutative Z7'-Spaces 141
537 Gateaux and Frechel/-Differentiable Functions 142
5 4 Taylor Approximation of Operator Functions 145
541 Taylor Remainders of Matrix Functions 145
542 Taylor Remainders for Perturbations in Sp and B('H) 149
543 Taylor Remainders for Unsummable Perturbations 153
5 5 Spectral Shift 154
551 Spectral Shift Function for Self-adjoint Operators 155
552 Spectral Shift Function for Nonself-adjoint Operators 162
553 Spectral Shift Measure in the Setting of von Neumann
Algebras 165
5 6 Spectral Flow 166
5 7 Quantum Differentiability 170
5 8 Differentiation of Noncommutative Lp-Norms 172
References 179 |
| any_adam_object | 1 |
| author | Skripka, Anna Tomskova, Anna ca. 20./21. Jahrhundert |
| author_GND | (DE-588)1202019110 (DE-588)1202614329 |
| author_facet | Skripka, Anna Tomskova, Anna ca. 20./21. Jahrhundert |
| author_role | aut aut |
| author_sort | Skripka, Anna |
| author_variant | a s as a t at |
| building | Verbundindex |
| bvnumber | BV046322831 |
| classification_rvk | SI 850 SK 620 |
| ctrlnum | (OCoLC)1134789417 (DE-599)HBZHT020318728 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV046322831</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200115</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">200108s2019 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783030324056</subfield><subfield code="9">978-3-030-32405-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1134789417</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT020318728</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-83</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47B49</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46L51</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Skripka, Anna</subfield><subfield code="0">(DE-588)1202019110</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Multilinear operator integrals</subfield><subfield code="b">theory and applications</subfield><subfield code="c">Anna Skripka, Anna Tomskova</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham, Switzerland</subfield><subfield code="b">Springer</subfield><subfield code="c">[2019]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xi, 190 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2250</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integraloperator</subfield><subfield code="0">(DE-588)4131247-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Multilineare Abbildung</subfield><subfield code="0">(DE-588)4479794-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Operatortheorie</subfield><subfield code="0">(DE-588)4075665-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Operatortheorie</subfield><subfield code="0">(DE-588)4075665-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Integraloperator</subfield><subfield code="0">(DE-588)4131247-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Multilineare Abbildung</subfield><subfield code="0">(DE-588)4479794-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tomskova, Anna</subfield><subfield code="d">ca. 20./21. Jahrhundert</subfield><subfield code="0">(DE-588)1202614329</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-030-32406-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2250</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2250</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">V:DE-605;X:semantics</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://digitale-objekte.hbz-nrw.de/storage2/2019/12/22/file_27/8797916.pdf</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031699816&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-031699816</subfield></datafield></record></collection> |
| id | DE-604.BV046322831 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-31T19:02:44Z |
| institution | BVB |
| isbn | 9783030324056 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031699816 |
| oclc_num | 1134789417 |
| open_access_boolean | |
| owner | DE-83 DE-824 DE-188 |
| owner_facet | DE-83 DE-824 DE-188 |
| physical | xi, 190 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Skripka, Anna (DE-588)1202019110 aut Multilinear operator integrals theory and applications Anna Skripka, Anna Tomskova Cham, Switzerland Springer [2019] xi, 190 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2250 Integraloperator (DE-588)4131247-8 gnd rswk-swf Multilineare Abbildung (DE-588)4479794-1 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Integraloperator (DE-588)4131247-8 s Multilineare Abbildung (DE-588)4479794-1 s DE-604 Tomskova, Anna ca. 20./21. Jahrhundert (DE-588)1202614329 aut Erscheint auch als Online-Ausgabe 978-3-030-32406-3 Lecture notes in mathematics 2250 (DE-604)BV000676446 2250 V:DE-605;X:semantics application/pdf http://digitale-objekte.hbz-nrw.de/storage2/2019/12/22/file_27/8797916.pdf Inhaltsverzeichnis HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031699816&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skripka, Anna Tomskova, Anna ca. 20./21. Jahrhundert Multilinear operator integrals theory and applications Lecture notes in mathematics Integraloperator (DE-588)4131247-8 gnd Multilineare Abbildung (DE-588)4479794-1 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4131247-8 (DE-588)4479794-1 (DE-588)4075665-8 |
| title | Multilinear operator integrals theory and applications |
| title_auth | Multilinear operator integrals theory and applications |
| title_exact_search | Multilinear operator integrals theory and applications |
| title_full | Multilinear operator integrals theory and applications Anna Skripka, Anna Tomskova |
| title_fullStr | Multilinear operator integrals theory and applications Anna Skripka, Anna Tomskova |
| title_full_unstemmed | Multilinear operator integrals theory and applications Anna Skripka, Anna Tomskova |
| title_short | Multilinear operator integrals |
| title_sort | multilinear operator integrals theory and applications |
| title_sub | theory and applications |
| topic | Integraloperator (DE-588)4131247-8 gnd Multilineare Abbildung (DE-588)4479794-1 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Integraloperator Multilineare Abbildung Operatortheorie |
| url | http://digitale-objekte.hbz-nrw.de/storage2/2019/12/22/file_27/8797916.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031699816&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT skripkaanna multilinearoperatorintegralstheoryandapplications AT tomskovaanna multilinearoperatorintegralstheoryandapplications |
Es ist kein Print-Exemplar vorhanden.
Inhaltsverzeichnis