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Extreme points for convex mappings ofB n

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Abstract

We exhibit a collection of extreme points of the family of normalized convex mappings of the open unit ball of ℂn forn≥2. These extreme points are defined in terms of the extreme points of a closed ball in the Banach space of homogeneous polynomials of degree 2 in ℂn−1, which are fully classified. Two examples are given to show that there are more convex mappings than those contained in the closed convex hull of the set of extreme points here exhibited.

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Authors and Affiliations

  1. Department of Mathematics, University of Scranton, 18510, Scranton, PA, USA

    Jerry R. Muir

  2. Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA

    Ted J. Suffridge

Authors
  1. Jerry R. Muir
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  2. Ted J. Suffridge
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Correspondence to Jerry R. Muir.

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Muir, J.R., Suffridge, T.J. Extreme points for convex mappings ofB n . J. Anal. Math. 98, 169–182 (2006). https://doi.org/10.1007/BF02790274

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  • DOI: https://doi.org/10.1007/BF02790274

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