Zb. Hu et D. Mupasiri, COMPLEX STRONGLY EXTREME-POINTS IN QUASI-NORMED SPACES, Journal of mathematical analysis and applications, 204(2), 1996, pp. 522-544
We study the complex strongly extreme points of (bounded) subsets of c
ontinuously quasi-normed vector spaces X over C. When X is a complex n
ormed linear space, these points are the complex analogues of the fami
liar (real) strongly extreme points. We show that if X is a complex Ba
nach space then the complex strongly extreme points of B-X admit sever
al equivalent formulations some of which are in terms of ''pointwise''
versions of well known moduli of complex convexity, We use this resul
t to obtain a characterization of the: complex extreme points of B(lp(
Xj)j is an element of I) and BL(p(mu,X)) where 0<p<infinity, X and eac
h X(j), j is an element of I, are complex Banach spaces. (C) 1996 Acad
emic Press, Inc.