Ideal spaces are a very general class of normed spaces of measurable functions, which includes e.g. Lebesgue and Orlicz spaces. Their most important application is in functional analysis in the theory of (usual and partial) integral and integro-differential equations. The book is a rather complete and self-contained introduction into the general theory of ideal spaces. Some emphasis is put on spaces of vector-valued functions and on the constructive viewpoint of the theory (without the axiom of choice). The reader should have basic knowledge in functional analysis and measure theory.

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Bibliographic Information

Book Title: Ideal Spaces
Authors: Martin Väth
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0093548
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1997
Softcover ISBN: 978-3-540-63160-6Published: 17 July 1997
eBook ISBN: 978-3-540-69192-1Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VI, 150
Topics: Functional Analysis, Real Functions, Mathematical Logic and Foundations

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Table of contents (5 chapters)

Front Matter

Introduction

Basic definitions and properties

Ideal spaces with additional properties

Ideal spaces on product measures and calculus

Operators and applications

Back Matter

About this book