PROJECTIONS ONTO SYMMETRIC SPACES

Abstract

The projection constants λ(X _n) of real n-dimensional symmetric spaces X _n satisfy asymptotically λ(X _n) ⪯ √n—4/√n which is smaller than for general spaces. For small dimensions, specific numerical values are obtained. For n = 2, we reprove the result of D.R. Lewis that λ(X ₂) ⪯ λ(l² ₂) = 4/π for 2-dimensional symmetric spaces. If n > 2, however, λ(X _n) is generally larger than λ(lⁿ ₂) for symmetric spaces. The method used is based on trace-duality and estimates involving symmetrically invariant spherical functions.