Derived Functors in Functional Analysis Book

1 Introduction 1

2 Notions from homological algebra 7

2.1 Derived Functors 7

2.2 The category of locally convex spaces 13

3 The projective limit functor for countable spectra 17

3.1 Projective limits of linear spaces 17

3.2 The Mittag-Leffler procedure 23

3.3 Projective limits of locally convex spaces 38

3.4 Some Applications 50

3.4.1 The Mittag-Leffler theorem 50

3.4.2 Separating singularities 51

3.4.3 Surjectivity of the Cauchy-Riemann operator 51

3.4.4 Surjectivity of P(D) on spaces of smooth functions 52

3.4.5 Surjectivity of P(D) the space of distributions 52

3.4.6 Differential operators for ultradifferentiable functions of Roumieu type 54

4 Uncountable projective spectra 59

4.1 Projective spectra of linear spaces 59

4.2 Insertion: The completion functor 68

4.3 Projective spectra of locally convex spaces 70

5 The derived functors of Hom 77

5.1 Extk in the category of locally convex spaces 77

5.2 Splitting theory for Fréchet spaces 86

5.3 Splitting in the category of (PLS)-spaces 96

6 Inductive spectra of locally convex spaces 109

7 The duality functor 119

References 129

Index