Projection constants of symmetric spaces and variants of Khintchine's inequality

The projection constants ofthe lpn-spaces for 1 less than or equal to p les s than or equal to 2 satisfy lambda(lpn)/root n --> c with c = 2/pi in the real case an c = root pi/2 in the complex case. Further, there is c < 1 suc h that the projection constant of any n-dimensional space Xn with 1-symmetr ic basis can be estimated by lambda(Xn) less than or equal to c root n. The proofs of the results are based on averaging techniques over permutations and a variant of Khintchine's inequality which states that [GRAPHICS]