Anzeige
Erschienen in:
2013 | OriginalPaper | Buchkapitel
5. Mapping Cones
verfasst von : Erling Størmer
Erschienen in: Positive Linear Maps of Operator Algebras
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.