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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
Rights Information: Copyright 1995 Kang, Jeongheung
Date Available in IDEALS: 2011-05-07
Identifier in Online Catalog: AAI9522128
OCLC Identifier: (UMI)AAI9522128

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