Abstract
In order to group together maps with similar properties we introduce certain convex cones of positive maps of the bounded operators B(H) on a Hilbert space into itself, called mapping cones. Then we define positivity of a map of a C ∗-algebra into B(H) with respect to a mapping cone and show the basic properties of this positivity concept. For example we see that positivity for a map with respect to the smallest mapping cone is equivalent to its dual functional being a positive multiple of a separable state. We conclude by showing a Hahn-Banach type extension theorem for maps positive with respect to a mapping cone.
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Størmer, E. (2013). Mapping Cones. In: Positive Linear Maps of Operator Algebras. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34369-8_5
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DOI: https://doi.org/10.1007/978-3-642-34369-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34368-1
Online ISBN: 978-3-642-34369-8
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