Pre-Riesz Spaces
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Pre-Riesz Spaces

Anke Kalauch, Onno van Gaans

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  1. 314 pages
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eBook - ePub

Pre-Riesz Spaces

Anke Kalauch, Onno van Gaans

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About This Book

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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Information

Publisher
De Gruyter
Year
2018
ISBN
9783110475449
Edition
1
Topic
Mathematics
Subtopic
Functional Analysis
Index
Mathematics

Table of contents