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

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.


Existence Result Positive Operator Banach Lattice Real Banach Space Subspace Versus 
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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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