Geometrical and Martingale characterizations of UMD and Hilbert spaces

Suppose that X is a real or complex Banach space with norm $\vert \cdot \vert$. Then X is a Hilbert space if and only if $E\vert x + Y\vert \geq 1$ for all x $\in$ X and all X-valued Bochner integrable functions Y on the Lebesgue unit interval satisfying EY = 0 and $\vert Y\vert \geq$ 1 a.e. This leads to a simple proof of the biconvex-function characterization due to Burkholder.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Lee, Jinsik Mok

Contributors dc:contributor

• Burkholder, Donald L.

• Mathematics

Statement dc:rights

• Copyright 1992 Lee, Jinsik Mok

Language dc:language

eng

Identifier

AAI9215847
(UMI)AAI9215847

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23039