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manuscripta mathematica

, Volume 5, Issue 2, pp 113–122 | Cite as

Strongly extreme points in Banach spaces

  • Robert McGuigan
Article

Abstract

In this paper some properties of a special type of boundary point of convex sets in Banach spaces are studied. Specifically, a strongly extreme point x of a convex set S is a point of S such that for each real number r>0, segments of length 2r and centered x are not uniformly closer to S than some positive number d(x,r). Results are obtained comparing the notion of strongly extreme point to other known types of special boundary points of convex sets. Using the notion of strongly extreme point, a convexity condition is defined on the norm of the space under consideration, and this convexity condition makes possible a unified treatment of some previously studied convexity conditions. In addition, a sufficient condition is given on the norm of a separable conjugate space for every extreme point of the unit ball to be strongly extreme.

Keywords

Banach Space Real Number Number Theory Extreme Point Boundary Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Robert McGuigan
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherst

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