Interpolation functors and duality / Sten Kaijser, Joan Wick Pelletier

The duality theory of the classical (real and complex) interpolation methods for Banach spaces due to A. P. Calderón , J.-L. Lions , S. G. Kreĭn and J. Peetre has some well-known shortcomings. The purpose of this paper is to construct a somewhat extended theory of interpolation which contains the classical theory and which is more suitable for duality. From the introduction: "Compared to most other papers on interpolation theory … ours is probably the most categorical. We have used several important ideas from category theory … interpolation theory is so functorial in nature that category theory will lead to the correct notions.'' The book is directed to functional analysts (specializing in interpolation theory) and to category theorists "interested in applications of category methods to analysis.'' Contents: Part I (1. Preliminaries, 2. The real method, 3. The complex method), Part II (4. Categorical notions, 5. Finite-dimensional Doolittle diagrams, 6. Kan extensions, 7. Duality), Part III (8. More about duality, 9. The classical methods from a categorical viewpoint). (MathSciNet)