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$%A. Pietsch, About the Banach envelope of l1,∞ , Rev. Mat. Complut. 22 (2009), no. 1, 209–226.%$
We study the Banach envelope of the quasi-Banach space l1,∞ consisting of all sequences x = (ξk) with sn(x) = O, where sn(x) denotes the non-increasing rearrangement of x = (ξk). The situation turns out to be much more complicated than that in the well-known case of the separable subspace l1,∞, whose members are characterized by s n(x)=o.
Key words: Banach envelope, Marcinkiewicz space , weak -space.
2000 Mathematics Subject Classification: 46A16, 46B45.