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Positive Linear Maps of Operator Algebras

  • Kartonierter Einband
  • 144 Seiten
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This book covers the properties and structure of positive linear maps of operator algebras into the bounded operators on Hilbert s... Weiterlesen
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Beschreibung

This book covers the properties and structure of positive linear maps of operator algebras into the bounded operators on Hilbert space.

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 The author, a leading authority on the subject, sets out numerous results previously unpublished in book form.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.



Written by one of the founders of the theory of positive linear maps

First and only book in the literature devoted entirely to positive maps

Contains the necessary background to study the operator algebra part of quantum information theory ?



Autorentext
Stormer's area of work is operator algebras. His main specialties have been non-commutative ergodic theory and positive maps. In connection with the latter the author has also worked on Jordan algebras of self-adjoint operators. He has received the main prize from the Norwegian Science Foundation, the Möbius Prize.

Inhalt

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.

Produktinformationen

Titel: Positive Linear Maps of Operator Algebras
Autor:
EAN: 9783642429132
ISBN: 3642429130
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 144
Gewicht: 230g
Größe: H235mm x B155mm x T8mm
Jahr: 2015
Auflage: 2013

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