Pre-Riesz Spaces: 66 (De Gruyter Expositions in Mathematics, 66) - Hardcover

Kalauch; Anke; Van Gaans; Onno

Hardcover

ISBN 10: 3110475391 ISBN 13: 9783110475395

Publisher: De Gruyter, 2018

Synopsis

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

About this title

About the Author

Anke Kalauch, TU Dresden, Germany;
Otto van Gaans, Leiden University, The Netherlands.

Edition details

• Publisher: De Gruyter
• Publication date: 2018
• Language: English
• ISBN 10: 3110475391
• ISBN 13: 9783110475395
• Binding: Hardcover
• Edition number: 1
• Number of pages: 301