This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/19279
Description
Title
Complemented subspaces of weakL(1)
Author(s)
Kang, Jeongheung
Issue Date
1995
Doctoral Committee Chair(s)
Peck, Tenney
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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 $wL\sb{\1}.$
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.