Renormings via asymptotic uniform convexity and the approximation property on near Hilbertian spaces /
Let X be a Banach space and let ([], A, P) be the probability space with [] = {-1, 1}N , A the Borel []-algebra, and P the Haar measure on []. If the space of X-valued strongly-measurable Bochner-integrable functions Lr([], X), 1 < r [], has an equivalent asymp...
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
2001.
|
| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=725921551&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Let X be a Banach space and let ([], A, P) be the probability space with [] = {-1, 1}N , A the Borel []-algebra, and P the Haar measure on []. If the space of X-valued strongly-measurable Bochner-integrable functions Lr([], X), 1 < r [], has an equivalent asymptotically uniformly convex norm of power type p then X admits a uniformly convex renorming of power type. Using A. M. Davie's construction of a subspace of lp, p > 2, without the approximation property, it is shown that there exists an asymptotically Hilbertian space E which is 'almost' a weak Hilbert space and that fails the approximation property. In addition, the space E is a subspace of a space with an unconditional basis and can be written as the direct sum of two subspaces all of whose subspaces have the approximation property. |
|---|---|
| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | vi, 53 leaves ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 50-52). |