Contractive Projections in C p Jonathan Arazy and Yaakov Friedman Summary: Contractive Projections in C p Jonathan Arazy and Yaakov Friedman Contents: 0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. Properties of contractive projections on C p which depend on smoothness, strict convexity and reflexivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. JC \Lambda ­triples and the formulation of the main result . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3. Differentiation formulas and Schur multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4. Connection between a contractive projection and Pierce projections associated with elements in its range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5. Existence of atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6. Basic relations between atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 7. Structure of N­convex subspaces of C p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 8. Conclusion of the proof of the Main Theorem and applications . . . . . . . . . . . . . . 79 9. Families of contractive projections and concluding remarks . . . . . . . . . . . . . . . . . . 90 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 iii Abstract Collections: Mathematics