Ideals and bands in pre-Riesz spaces |
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Authors: | Onno van Gaans Anke Kalauch |
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Institution: | (1) Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands;(2) Institut für Analysis, Fachrichtung Mathematik, TU Dresden, 01062 Dresden, Germany |
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Abstract: | In a vector lattice, ideals and bands are well-investigated subjects. We study similar notions in a pre-Riesz space. The pre-Riesz
spaces are exactly the order dense linear subspaces of vector lattices. Restriction and extension properties of ideals, solvex
ideals and bands are investigated. Since every Archimedean directed partially ordered vector space is pre-Riesz, we establish
properties of ideals and bands in such spaces.
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Keywords: | Band disjointness ideal order dense subspace partially ordered vector space pre-Riesz space solvex ideal |
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