About the Banach Envelope of l1,∞ - Pietsch, Albrecht (Revista Matemática Complutense, 2009)
We study the Banach envelope of the quasi-Banach space l1,∞ consisting of all sequences x=(ξ k) with sn(x)=O(1/n), where (sn (x)) denotes the non-increasing rearrangement of x=(ξ k) The situation turns out to be much more complicated than that in the well-known case of the separable subspace lo1,∞, whose members are characterized by sn(x) =o(1/n).