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Positive linear extension operators for spaces of affine functions

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Abstract

The following result is proved: letE be anF-space (that is, the space of all continuous affine functions defined on a compact universal cap van shing at zero) and letMχE be anM-ideal. Then, ifE/M is a π1 with positive defining projections, then there is a positive linear operator ϱ:E/M→E of norm one such that ϱ lifts the canonical mapE→E/M. In the proof, which heavily depends on work of Ando, we study ensor products of certain convex cones with compact bases, and we calculate the norm of a positive linear operator defined on a finite dimensional space with range in aF-space. Various corollaries are deduced for split faces of compact convex sets and for morphisms ofC *-algebras.

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  1. Matematisk Institut, Aarhus Universitet, Aarhus, Denmark

    Jorgen Vesterstrom

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  1. Jorgen Vesterstrom
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Vesterstrom, J. Positive linear extension operators for spaces of affine functions. Israel J. Math. 16, 203–211 (1973). https://doi.org/10.1007/BF02757871

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  • DOI: https://doi.org/10.1007/BF02757871

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