Derived Functors in Functional Analysis

Introduction.- Notions from homological algebra: Derived Functors; The category of locally convex spaces.- The projective limit functor for countable spectra: Projective limits of linear spaces; The Mittag-Leffler procedure; Projective limits of locally convex spaces; Some Applications: The Mittag-Leffler theorem; Separating singularities; Surjectivity of the Cauchy-Riemann operator; Surjectivity of P(D) on spaces of smooth functions; Surjectivity of P(D) the space of distributions; Differential operators for ultradifferentiable functions of Roumieu type.- Uncountable projective spectra: Projective spectra of linear spaces; Insertion: The completion functor; Projective spectra of locally convex spaces.- 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.- Inductive spectra of locally convex spaces.- The duality functor.- References.- Index.