Shape-preserving projections in low-dimensional settings and the q -monotone case - Prophet, M. P.; Shevchuk, I. A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
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, шє 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 which (lacks structure and thus) serves as an application for our characterization.