An Introductory Course in Functional Analysis by Adam Bowers & Nigel J. Kalton (deceased)

Author:Adam Bowers & Nigel J. Kalton (deceased)
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

The function F is continuous with and . By the Intermediate Value Theorem, there exists a such that .

Let and . By the choice of τ, we have and . We have found distinct functions g and h in such that . Therefore, f is not an extreme point of the unit ball of . Since f was an arbitrary element of , we conclude that the unit ball in has no extreme points.

(iv) . We will show there are no extreme points in . Suppose is a sequence in . Then , and so there exists some such that . We will define sequences and in c 0 so that . If , then define y and z as follows:

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.