Subspaces of normed Riesz spaces (Q702026)

The author presents a characterization of a normed partially ordered vector space. He shows that a normed partially ordered vector space with a norm \(p\) is linearly, norm and order isomorphic to a subspace of a normed Riesz space (which is also a Riesz space) if and only if its positive cone is closed and \(p(x)\leq p(y)\) whenever \(-y\leq x\leq y\). He also gives a similar characterization of subspaces of \(M\)-normed Riesz spaces. Some properties concerning the norms following from the characterization theorem are investigated. Also, a generalization of the notion of Riesz norm is studied. He ends this work by giving a partial characterization of subspaces of Riesz spaces with Riesz seminorms.