Contractive Projections In $C_P$

Properties of contractive projections on Cp which depend on smoothness, strict convexity and reflexivity, JC*-triples and the formulation of the main result; Differentiation formulas and Schur multipliers; Connection between a contractive projection and Peirce projections associated with elements in its range; Existence of atoms; Basic relations between atoms; Structure of N-convex subspaces of Cp; Conclusion of the proof of the Main Theorem and applications, Families of contractive projections and concluding remarks.

This work is devoted to the study of contractive projection (that is, norm-one idempotent operators) on Cp where Cp denotes the von Meumann-Schatten p-classes. The authors show that the range of a contractive projection on Cp(1<p<<Pi1>?, p<Pi3>=2) is the direct sum of Cp-ideals of classical Cartan factors.