Complex strongly extreme points in quasi-normed spaces

We study the complex strongly extreme points of (bounded) subsets of continuously quasi-normed vector spaces X over C. When X is a complex normed linear 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-X admit several equivalent formulations some of which 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(lp(Xj)j is an element of I) and BL(p(mu,X)) where 0<p<infinity, X and each X(j), j is an element of I, are complex Banach spaces. (C) 1996 Academic Press, Inc.