Complemented subspaces of weakL(1)

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Title:	Complemented subspaces of weakL(1)
Author(s):	Kang, Jeongheung
Doctoral Committee Chair(s):	Peck, Tenney
Department / Program:	Mathematics
Discipline:	Mathematics
Degree Granting Institution:	University of Illinois at Urbana-Champaign
Degree:	Ph.D.
Genre:	Dissertation
Subject(s):	Mathematics
Abstract:	The Banach envelope of $weakL\sp1$ (denoted $wL\sb{\1})$ is a sort of universal Banach space for separable Banach spaces. In this paper, we can see the complemented Banach subspaces of $wL\sb{\1}.$ In particular, the space $wL\sb{\1}$ contains complemented Banach sublattices that are isometrically isomorphic $l\sp{p}\ (1 \le p < \infty)$ and $c\sb0.$ Moreover, if E is a separable reflexive Banach lattice, then the space $wL\sb{\1}$ contains a complemented sublattice that is isometrically isomorphic to E. Also we can see nonseparable complemented subspaces of $wL\sb{\1}.$ Finally, we show a couple of noncomplemented subspaces of $wL\sb{\1}.$
Issue Date:	1995
Type:	Text
Language:	English
URI:	http://hdl.handle.net/2142/19279
Rights Information:	Copyright 1995 Kang, Jeongheung
Date Available in IDEALS:	2011-05-07
Identifier in Online Catalog:	AAI9522128
OCLC Identifier:	(UMI)AAI9522128