Pre-Riesz Spaces / Anke Kalauch, Onno van Gaans.

Format:

Book

Author/Creator:

Kalauch, Anke, author.

van Gaans, Onno, author.

Series:

De Gruyter expositions in mathematics ; Volume 66.

De Gruyter Expositions in Mathematics ; 66

Language:

English

Subjects (All):

Riesz spaces.

Partially ordered spaces.

Vector spaces.

Physical Description:

1 online resource (304 pages).

Place of Publication:

Berlin ; Boston : De Gruyter, [2018]

Language Note:

In English.

Summary:

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

Contents:

Frontmatter

Contents

Preface

1. A primer on ordered vector spaces

2. Embeddings, covers, and completions

3. Seminorms on pre-Riesz spaces

4. Disjointness, bands, and ideals in pre-Riesz spaces

5. Operators on pre-Riesz spaces

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9783110475449

3110475448

9783110476293

3110476290

OCLC:

1049574525