Abstract
We prove a geometric version of an operator valued Hahn–Banach theorem and use it to study sets K that are A-convex over a unital C*-algebra A in the sense that \({\sum_{j=1}^{n} a_{j}^{*}y_{j}a_{j}\in K}\) whenever \({y_{j}\in K}\) and \({a_{j}\in A}\) with \({\sum_{j=1}^{n}a_{j}^{*}a_{j}=1}\). We show how weak* compact such sets can be realized as concrete sets of unital completely positive maps. An application to C*-extreme points is also presented.
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The author was supported in part by the Ministry of Science and Education of Slovenia.
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Magajna, B. C*-Convex Sets and Completely Positive Maps. Integr. Equ. Oper. Theory 85, 37–62 (2016). https://doi.org/10.1007/s00020-016-2291-4
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DOI: https://doi.org/10.1007/s00020-016-2291-4