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arXiv · 1807.01003

A short note on band projections in partially ordered vector spaces

Jochen Glück
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Abstract

Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we prove that the range of $P$ is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces.

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Jochen Glück. 2018-07-03. A short note on band projections in partially ordered vector spaces. https://arxiv.org/abs/1807.01003

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