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 |