Faculty Publications

Shape-Preserving Projections In Low-Dimensional Settings And The Q-Monotone Case

Document Type

Article

Journal/Book/Conference Title

Ukrainian Mathematical Journal

Volume

64

Issue

5

First Page

767

Last Page

780

Abstract

Let P:X → V be a projection from a real Banach space X onto a subspace V and let S ⊂ X. In this setting, one can ask if S is left invariant under P, i. e., if PS ⊂ S. If V is finite-dimensional and S is a cone with particular structure, then the occurrence of the imbedding PS ⊂ S 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 PS ⊂ S. We note that the (so-called) q-monotone shape forms a cone that (lacks structure and thus) serves as an application for our characterization. © 2012 Springer Science+Business Media New York.

Department

Department of Mathematics

Original Publication Date

10-1-2012

DOI of published version

10.1007/s11253-012-0677-2

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