Overview
- 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 ?
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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About this book
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 The author, a leading authority on the subject, sets out numerous results previously unpublished in book form.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.
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Table of contents (8 chapters)
Reviews
From the reviews:
“This book is a timely and valuable contribution to the theory and applications of positive linear maps defined on operator algebras and operator systems. … The style of writing is succinct and to the point. … the book’s value is in its content, the vast majority of which cannot be found in other monographs, and it will surely become the essential reference on positive linear maps for mathematicians and physicists alike.” (Douglas R. Farenick, Mathematical Reviews, January, 2014)
“The author, who is a reputed researcher in this discipline, gathers in this book the main results on positive operators between C*-algebras with the additional novelty of inserting results never before collected together in a book. … This book is … a very interesting contribution to the theory of positive linear maps from its beginnings to the latest results. It makes for interesting reading both from a mathematical point of view, as well as for those who are interested in quantum information theory.” (Antonio M. Peralta, zbMATH, Vol. 1269, 2013)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Positive Linear Maps of Operator Algebras
Authors: Erling Størmer
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-642-34369-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-34368-1Published: 14 December 2012
Softcover ISBN: 978-3-642-42913-2Published: 29 January 2015
eBook ISBN: 978-3-642-34369-8Published: 13 December 2012
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: VIII, 136
Topics: Functional Analysis, Linear and Multilinear Algebras, Matrix Theory, Mathematical Methods in Physics