Positive Linear Maps of Operator Algebras

  • Erling Størmer
Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Erling Størmer
    Pages 1-12
  3. Erling Størmer
    Pages 13-26
  4. Erling Størmer
    Pages 27-47
  5. Erling Størmer
    Pages 49-62
  6. Erling Størmer
    Pages 63-73
  7. Erling Størmer
    Pages 75-93
  8. Erling Størmer
    Pages 95-111
  9. Erling Størmer
    Pages 113-119
  10. Back Matter
    Pages 121-134

About this book

Introduction

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 The author, a leading authority on the subject, sets out numerous results previously unpublished in book form.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

 

Keywords

Choi matrices Jordan Algebras Positive maps completely positive maps mapping cones

Authors and affiliations

  • Erling Størmer
    • 1
  1. 1.Department of MathematicsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-34369-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-34368-1
  • Online ISBN 978-3-642-34369-8
  • Series Print ISSN 1439-7382