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

• Date: 2012
• Main Authors: Prophet, M. P., Shevchuk, I. A., Профет, М. П., Шевчук, І. О.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2607
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $P: X \rightarrow V$ be a projection from a real Banach space $X$ onto a subspace $V$ and let $S \subset X$. In this setting, one can ask if $S$ is left invariant under $P$, i.e., if $PS \subset S$. If $V$ is finite-dimensional and $S$ is a cone with particular structure, then the occurrence o...