复线性空间上凸函数的支撑泛函

Complex Support Functionals for Convex Functions

采用子空间中支撑泛函延拓的方法,构造出在复线性空间任意点上的复支撑泛函;确定在同一支撑点上复支撑泛函的数值域,从而得到复支撑泛函具有唯一性的充分必要条件。

This paper investigates the existence of complex support functional of a convex function in complex linear spaces and the complex numerical ranges of the complex support functionals on a point. Complex support functionals with function extension are constructed and the complex numerical ranges of all complex support functionals on a support point are established. And a necessary and sufficient condition ensuring that the complex support functional on a support point is unique has been presented.