| 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 |
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