Hausdorff Spectra in Functional Analysis [Hardcover]

Self-contained, and collating for the first time material that has until now only been published in journals - often in Russian - this book will be of interest to functional analysts, especially those with interests in topological vector spaces, and to algebraists concerned with category theory. The closed graph theorem is one of the corner stones of functional analysis, both as a tool for applications and as an object for research. However, some of the spaces which arise in applications and for which one wants closed graph theorems are not of the type covered by the classical closed graph theorem of Banach or its immediate extensions. To remedy this, mathematicians such as Schwartz and De Wilde (in the West) and Rajkov (in the East) have introduced new ideas which have allowed them to establish closed graph theorems suitable for some of the desired applications. In this book, Professor Smirnov uses category theory to provide a very general framework, including the situations discussed by De Wilde, Rajkov and others. General properties of the spaces involved are discussed and applications are provided in measure theory, global analysis and differential equations.Introduction
Infra-Additive Functionals in Analysis
Some Applictions of Hausdorff Limits and H-spaces
Hausdorff Spectrum Functors
The H-Limit of a Hausdorff Spectrum in a Semiabelian Category G
Exact Sequences of Hausdorff Spectra
Glossary
References
Subject Index
Collates and presents for the first time material that has previously only been available in journals
Introduces new concepts of functional analysis (Hausdorff spectrum and Hausdorff limit)This book is a self-contained introduction to new concepts of functional analysis collating for the first time material, published mostly in journals, that libraries will not have.