Full paper in PDF format:
$%A. Pietsch, About the Banach envelope of l1,∞ , Rev. Mat. Complut. 22 (2009), no. 1, 209–226.%$

About the Banach Envelope of l1,∞
Albrecht PIETSCH
Biberweg 7
07749 Jena — Germany
pietsch@minet.uni-jena.de

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

ABSTRACT

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 n).

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