The unit ball of the predual of $H^\infty(\mathbb{B}_d)$ has no extreme points

TL;DR

This paper proves that the predual of the space of bounded holomorphic functions on the unit ball in complex space has no extreme points in its unit ball, revealing a fundamental geometric property.

Contribution

It identifies the exposed points of the dual of the ball algebra and establishes that the predual of $H^ fty(B_d)$ lacks extreme points in its unit ball.

Findings

The unit ball of the dual of the ball algebra has identified exposed points.

The predual of $H^ fty(B_d)$ has no extreme points in its unit ball.

The result clarifies the geometric structure of the predual space.

Abstract

We identify the exposed points of the unit ball of the dual space of the ball algebra. As a corollary, we show that the predual of $H^\infty(\mathbb{B}_d)$ has no extreme points in its unit ball.