Shape-preserving projections in low-dimensional settings and the q-monotone case
Ukrainian Mathematical Journal
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.
Original Publication Date
DOI of published version
Prophet, M. P. and Shevchuk, I. A., "Shape-preserving projections in low-dimensional settings and the q-monotone case" (2012). Faculty Publications. 1737.