Derived Functors in Functional Analysis

✍ Scribed by Jochen Wengenroth (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 139
• Series: Lecture Notes in Mathematics 1810
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

1. Introduction....Pages 1-6
   2. Notions from homological algebra....Pages 7-15
   3. The projective limit functor for countable spectra....Pages 17-57
   4. Uncountable projective spectra....Pages 59-76
   5. The derived functors of Hom....Pages 77-107
   6. Inductive spectra of locally convex spaces....Pages 109-118
   7. The duality functor....Pages 119-127
   References....Pages 129-132
   Index....Pages 133-134
   

✦ Subjects

Functional Analysis; Category Theory, Homological Algebra; Partial Differential Equations