Complex Strongly Extreme Points in Quasi-Normed Spaces

AbstractWe study the complex strongly extreme points of (bounded) subsets of continuously quasi-normed vector spacesXoverC. WhenXis a complex normed linear space, these points are the complex analogues of the familiar (real) strongly extreme points. We show that ifXis a complex Banach space then the complex strongly extreme points ofBXadmit 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 ofBlp(Xj)j∈IandBLp(μ,X)where 0<p<∞,Xand eachXj,j∈I, are complex Banach spaces