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Complex Strongly Extreme Points in Quasi-Normed Spaces

✍ Scribed by Zhibao Hu; Douglas Mupasiri

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 247 KB
Volume: 204
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0452

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✦ Synopsis

We study the complex strongly extreme points of bounded subsets of continuously quasi-normed vector spaces X over ‫.ރ‬ When X is a complex normed linear Ž . space, these points are the complex analogues of the familiar real strongly extreme points. We show that if X is a complex Banach space then the complex strongly extreme points of B admit several equivalent formulations some of which X are in terms of ''pointwise'' versions of well known moduli of complex convexity. We use this result to obtain a characterization of the complex extreme points of B and B where 0p -ϱ, X and each X , j g I, are complex l Ž X . L Ž , X . j p j jgI p Banach spaces.

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