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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

  

Source: Arazy, Jonathan - Department of Mathematics, University of Haifa

 

Collections: Mathematics