The Rademacher Projection

Part of the Lecture Notes in Mathematics book series (LNM, volume 1200)


In this chapter we return to the subject of estimating the norm of Rad n — the natural projection onto the subspace {Σ i=1 n r i (t)x i ; x i X} of L 2 (X). The main theorem here (14.5), due to Pisier, states that supn<∞Rad n ‖ < ∞ if and only if ℓ1 is not finitely representable in X. Towards the end of the chapter we give also an estimate for ‖Rad n ‖ good for any finite dimensional normed space. In this chapter it will be more convenient for us to work with complex scalars so we assume all spaces are over the complex field ℂ. (The results are easily seen to hold also in the real case)


Banach Space Real Case Natural Projection Complex Scalar Extension Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

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