COMPLEX STRONGLY EXTREME-POINTS IN QUASI-NORMED SPACES

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.