Extremal multipliers of the Drury-Arveson space

TL;DR

This paper characterizes quasi-extreme multipliers of the Drury-Arveson space and establishes that they are exactly the extreme points of the space's multiplier algebra unit ball.

Contribution

It provides a new characterization of quasi-extreme multipliers and proves their equivalence to extreme points in the multiplier algebra.

Findings

Quasi-extreme multipliers are characterized in a new way.

All quasi-extreme multipliers are extreme points of the multiplier algebra.

The paper links quasi-extremity with extremality in the unit ball.

Abstract

We give a new characterization of the so-called quasi-extreme multipliers of the Drury-Arveson space $H^2_d$, and show that every quasi-extreme multiplier is an extreme point of the unit ball of the multiplier algebra of $H^2_d$.