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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"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)