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$%A. Pietsch, About the Banach envelope of l1, , Rev. Mat. Complut. 22 (2009), no. 1, 209–226.%$

About the Banach Envelope of l1,
Albrecht PIETSCH
Biberweg 7
07749 Jena — Germany


Received: June 10, 2008
Accepted: September 30, 2008


We study the Banach envelope of the quasi-Banach space l1, consisting of all sequences x = (ξk) with sn(x) = O(1
n), 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(-1

Key words: Banach envelope, Marcinkiewicz space l1,∞ , weak l1  -space.
2000 Mathematics Subject Classification:
46A16, 46B45.