Pre-Riesz Spaces 1st Edition
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Pre-Riesz Spaces 1st Edition

SKU: 9783110475449

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Additional information

Full Title

Pre-Riesz Spaces 1st Edition
Author(s)

Anke Kalauch, Onno van Gaans
Edition

1st Edition
ISBN

9783110475449, 9783110475395, 9783110476293
Publisher

De Gruyter
Format

PDF and EPUB

Description

This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces

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