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Ukrainian Mathematical Journal

, Volume 64, Issue 5, pp 767–780 | Cite as

Shape-preserving projections in low-dimensional settings and the q-monotone case

  • M. P. Prophet
  • I. A. Shevchuk
Article
  • 43 Downloads

Let P:XV be a projection from a real Banach space X onto a subspace V and let SX. In this setting, one can ask if S is left invariant under P, i.e., if PSS. If V is finite-dimensional and S is a cone with particular structure, then the occurrence of the imbedding PSS can be characterized through a geometric description. This characterization relies heavily on the structure of S, or, more specifically, on the structure of the cone S * dual to S. In this paper, we remove the structural assumptions on S * and characterize the cases where PSS. We note that the (so-called) q-monotone shape forms a cone that (lacks structure and thus) serves as an application for our characterization.

Keywords

Existence Result Positive Operator Banach Lattice Real Banach Space Subspace Versus 
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 Science+Business Media New York 2012

Authors and Affiliations

  • M. P. Prophet
    • 1
  • I. A. Shevchuk
    • 2
  1. 1.University of Northern IowaCedar FallsUSA
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

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