Pre-Riesz Spaces

¡
¡ De Gruyter Expositions in Mathematics āĻŦāĻ‡ 66 ¡ Walter de Gruyter GmbH & Co KG
āĻ‡-āĻŦā§āĻ•
314
āĻĒā§ƒāĻˇā§āĻ āĻž
āĻ°ā§‡āĻŸāĻŋāĻ‚ āĻ“ āĻ°āĻŋāĻ­āĻŋāĻ‰ āĻ¯āĻžāĻšāĻžāĻ‡ āĻ•āĻ°āĻž āĻšā§ŸāĻ¨āĻŋ  āĻ†āĻ°āĻ“ āĻœāĻžāĻ¨ā§āĻ¨

āĻāĻ‡ āĻ‡-āĻŦā§āĻ•ā§‡āĻ° āĻŦāĻŋāĻˇā§Ÿā§‡

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

āĻ˛ā§‡āĻ–āĻ• āĻ¸āĻŽā§āĻĒāĻ°ā§āĻ•ā§‡

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

āĻ‡-āĻŦā§āĻ•ā§‡ āĻ°ā§‡āĻŸāĻŋāĻ‚ āĻĻāĻŋāĻ¨

āĻ†āĻĒāĻ¨āĻžāĻ° āĻŽāĻ¤āĻžāĻŽāĻ¤ āĻœāĻžāĻ¨āĻžāĻ¨āĨ¤

āĻĒāĻ āĻ¨ āĻ¤āĻĨā§āĻ¯

āĻ¸ā§āĻŽāĻžāĻ°ā§āĻŸāĻĢā§‹āĻ¨ āĻāĻŦāĻ‚ āĻŸā§āĻ¯āĻžāĻŦāĻ˛ā§‡āĻŸ
Android āĻāĻŦāĻ‚ iPad/iPhone āĻāĻ° āĻœāĻ¨ā§āĻ¯ Google Play āĻŦāĻ‡ āĻ…ā§āĻ¯āĻžāĻĒ āĻ‡āĻ¨āĻ¸ā§āĻŸāĻ˛ āĻ•āĻ°ā§āĻ¨āĨ¤ āĻāĻŸāĻŋ āĻ†āĻĒāĻ¨āĻžāĻ° āĻ…ā§āĻ¯āĻžāĻ•āĻžāĻ‰āĻ¨ā§āĻŸā§‡āĻ° āĻ¸āĻžāĻĨā§‡ āĻ…āĻŸā§‹āĻŽā§‡āĻŸāĻŋāĻ• āĻ¸āĻŋāĻ™ā§āĻ• āĻšā§Ÿ āĻ“ āĻ†āĻĒāĻ¨āĻŋ āĻ…āĻ¨āĻ˛āĻžāĻ‡āĻ¨ āĻŦāĻž āĻ…āĻĢāĻ˛āĻžāĻ‡āĻ¨ āĻ¯āĻžāĻ‡ āĻĨāĻžāĻ•ā§āĻ¨ āĻ¨āĻž āĻ•ā§‡āĻ¨ āĻ†āĻĒāĻ¨āĻžāĻ•ā§‡ āĻĒā§œāĻ¤ā§‡ āĻĻā§‡ā§ŸāĨ¤
āĻ˛ā§āĻ¯āĻžāĻĒāĻŸāĻĒ āĻ“ āĻ•āĻŽā§āĻĒāĻŋāĻ‰āĻŸāĻžāĻ°
Google Play āĻĨā§‡āĻ•ā§‡ āĻ•ā§‡āĻ¨āĻž āĻ…āĻĄāĻŋāĻ“āĻŦā§āĻ• āĻ†āĻĒāĻ¨āĻŋ āĻ•āĻŽā§āĻĒāĻŋāĻ‰āĻŸāĻžāĻ°ā§‡āĻ° āĻ“ā§Ÿā§‡āĻŦ āĻŦā§āĻ°āĻžāĻ‰āĻœāĻžāĻ°ā§‡ āĻļā§āĻ¨āĻ¤ā§‡ āĻĒāĻžāĻ°ā§‡āĻ¨āĨ¤
eReader āĻāĻŦāĻ‚ āĻ…āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ āĻĄāĻŋāĻ­āĻžāĻ‡āĻ¸
Kobo eReaders-āĻāĻ° āĻŽāĻ¤ā§‹ e-ink āĻĄāĻŋāĻ­āĻžāĻ‡āĻ¸ā§‡ āĻĒāĻĄāĻŧāĻ¤ā§‡, āĻ†āĻĒāĻ¨āĻžāĻ•ā§‡ āĻāĻ•āĻŸāĻŋ āĻĢāĻžāĻ‡āĻ˛ āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ“ āĻ†āĻĒāĻ¨āĻžāĻ° āĻĄāĻŋāĻ­āĻžāĻ‡āĻ¸ā§‡ āĻŸā§āĻ°āĻžāĻ¨ā§āĻ¸āĻĢāĻžāĻ° āĻ•āĻ°āĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤ āĻŦā§āĻ¯āĻŦāĻšāĻžāĻ°āĻ•āĻžāĻ°ā§€āĻ° āĻ‰āĻĻā§āĻĻā§‡āĻļā§āĻ¯ā§‡ āĻ¤ā§ˆāĻ°āĻŋ āĻ¸āĻšāĻžā§ŸāĻ¤āĻž āĻ•ā§‡āĻ¨ā§āĻĻā§āĻ°āĻ¤ā§‡ āĻĻā§‡āĻ“ā§ŸāĻž āĻ¨āĻŋāĻ°ā§āĻĻā§‡āĻļāĻžāĻŦāĻ˛ā§€ āĻ…āĻ¨ā§āĻ¸āĻ°āĻŖ āĻ•āĻ°ā§‡ āĻ¯ā§‡āĻ¸āĻŦ eReader-āĻ āĻĢāĻžāĻ‡āĻ˛ āĻĒāĻĄāĻŧāĻž āĻ¯āĻžāĻŦā§‡ āĻ¸ā§‡āĻ–āĻžāĻ¨ā§‡ āĻŸā§āĻ°āĻžāĻ¨ā§āĻ¸āĻĢāĻžāĻ° āĻ•āĻ°ā§āĻ¨āĨ¤