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lgli/M_Mathematics/MC_Calculus/MCf_Functional analysis/Stormer E. Positive linear maps of operator algebras (Springer, 2013)(ISBN 9783642343681)(O)(135s)_MCf_.pdf
Positive Linear Maps of Operator Algebras Springer Monographs in Mathematics 🔍
Stormer E. Springer Berlin Heidelberg : Imprint : Springer, Springer Monographs in Mathematics, 1st ed. 2013, Berlin, Heidelberg :, 2013
英语 [en] · PDF · 0.8MB · 2013 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/zlib · Save
描述
This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps' positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today's quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout. .
备用文件名
lgrsnf/M_Mathematics/MC_Calculus/MCf_Functional analysis/Stormer E. Positive linear maps of operator algebras (Springer, 2013)(ISBN 9783642343681)(O)(135s)_MCf_.pdf
备用文件名
nexusstc/Positive linear maps of operator algebras/44486d239375c5addc785b79a6bc581c.pdf
备用文件名
zlib/Mathematics/Stormer E./Positive linear maps of operator algebras_2079285.pdf
备选作者
by Erling Størmer
备选作者
Størmer, Erling
备用出版商
Spektrum Akademischer Verlag. in Springer-Verlag GmbH
备用出版商
Springer-Verlag Berlin and Heidelberg GmbH &
备用出版商
Steinkopff. in Springer-Verlag GmbH
备用版本
Springer Monographs in Mathematics, Berlin, Heidelberg, Germany, 2013
备用版本
Springer Nature, Berlin, 2013
备用版本
Heidelberg ; London, 2012
备用版本
Germany, Germany
备用版本
2013, 2012
元数据中的注释
Kolxo3 -- 63-64
元数据中的注释
lg925180
元数据中的注释
{"edition":"2013","isbns":["3642343686","3642343694","9783642343681","9783642343698"],"last_page":142,"publisher":"Springer","series":"Springer Monographs in Mathematics"}
元数据中的注释
MiU
备用描述
Cover......Page 1
Positive Linear Maps of Operator Algebras......Page 3
Introduction......Page 5
Contents......Page 7
1.1 Basic Definitions......Page 9
1.2 Completely Positive Maps......Page 10
1.3 Inequalities......Page 17
1.4 The Adjoint Map......Page 18
1.5 Notes......Page 19
2.1 Jordan Properties of Positive Maps......Page 21
2.2 Projection Maps......Page 25
2.3 Spin Factors......Page 30
2.4 Notes......Page 34
3.1 General Properties of Extremal Maps......Page 35
3.2 Jordan Homomorphisms......Page 38
3.3 Maps which Preserve Vector States......Page 42
3.4 Nonextendible Maps......Page 48
3.5 A Radon-Nikodym Theorem......Page 52
3.6 Notes......Page 55
4.1 The Choi Matrix......Page 56
4.2 The Dual Functional of a Map......Page 64
4.3 Notes......Page 68
5.1 Basic Properties......Page 70
5.2 The Extension Theorem......Page 77
5.3 Notes......Page 80
6.1 Basic Results......Page 81
6.2 Examples of Dual Cones......Page 86
6.3 Maps on the 2x2 Matrices......Page 89
6.4 Tensor Products......Page 96
6.5 Notes......Page 99
7.1 Positivity Properties of Linear Functionals......Page 100
7.2 PPT-States......Page 102
7.3 The Choi Map......Page 103
7.4 Entanglement......Page 107
7.5 Super-positive Maps......Page 110
7.6 Notes......Page 115
8.1 Norms of Maps......Page 117
8.2 Notes......Page 123
A1.3......Page 124
A1.5......Page 125
A.2 Tensor Products......Page 126
A.3 An Extension Theorem......Page 127
References......Page 129
List of Notations......Page 133
Index......Page 134
备用描述
Introduction.- 1 Generalities for positive maps.- 2 Jordan algebras and projection maps.- 3 Extremal positive maps.- 4 Choi matrices and dual functionals.- 5 Mapping cones.- 6 Dual cones.- 7 States and positive maps.- 8 Norms of positive maps.- Appendix: A.1 Topologies on B(H).- A.2 Tensor products.- A.3 An extension theorem.- Bibliography.- Index
备用描述
<p>Introduction
1 Generalities for positive maps
2 Jordan algebras and projection maps
3 Extremal positive maps
4 Choi matrices and dual functionals
5 Mapping cones
6 Dual cones
7 States and positive maps
8 Norms of positive maps
Appendix: A.1 Topologies on B(H)
A.2 Tensor products
A.3 An extension theorem
Bibliography
Index​.</p>.
备用描述
1. Generalities For Positive Maps -- 2. Jordan Algebras And Projection Maps -- 3. Extremal Positive Maps -- 4. Choi Matrices And Dual Functionals -- 5. Mapping Cones -- 6. Dual Cones -- 7. States And Positive Maps -- 8. Norms Of Positive Maps -- Appendix. Erling Størmer. Includes Bibliographical References (p. 127-130) And Index.
备用描述
Springer Monographs in Mathematics
Erscheinungsdatum: 14.12.2012
开源日期
2013-05-29
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