Derived Functors in Functional Analysis

Jochen Wengenroth

142 pages, parution le 18/02/2003

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Résumé

The text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext1 (E, F) for Fréchet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators.

The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program.

Contents

1- Introduction

2- Notions from homological algebra

Derived Functors
The category of locally convex spaces

3- The projective limit functor for countable spectra

Projective limits of linear spaces
The Mittag-Leffler procedure
Projective limits of locally convex spaces
Some Applications

4- Uncountable projective spectra

Projective spectra of linear spaces
Insertion: The completion functor
Projective spectra of locally convex spaces

5- The derived functors of Hom

Ext^k in the category of locally convex spaces
Splitting theory for Fréchet spaces
Splitting in the category of (PLS)-spaces

6- Inductive spectra of locally convex spaces

7- The duality functor

L'auteur - Jochen Wengenroth

University of Trier, Germany

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jochen Wengenroth
Parution	18/02/2003
Nb. de pages	142
Format	15,5 x 23,5
Couverture	Broché
Poids	224g
Intérieur	Noir et Blanc
EAN13	9783540002369