Noncoherence of the multiplier algebra of the Drury-Arveson space H^2_n for n>=3

TL;DR

This paper proves that for dimensions three and higher, the multiplier algebra of the Drury-Arveson space is not coherent, revealing a fundamental algebraic property of these function spaces.

Contribution

It establishes the noncoherence of the multiplier algebra M(H_n^2) for n>=3, a novel result in the understanding of these spaces' algebraic structure.

Findings

M(H_n^2) is not coherent for n>=3

The result impacts the theory of function spaces and operator algebras

Provides new insights into the algebraic properties of the Drury-Arveson space

Abstract

Let H_n^2 denote the Drury-Arveson Hilbert space on the unit ball B_n in C^n, and let M(H_n^2) be its multiplier algebra. We show that for n>=3, the ring M(H_n^2) is not coherent.