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

DOI10.7153/OAM-09-25zbMATH Open1317.47025arXiv1406.5934OpenAlexW2963250459MaRDI QIDQ5253054

Publication date: 4 June 2015

Published in: Operators and Matrices (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1406.5934

zbMATH Keywords

multiplier algebra Drury-Arveson space coherent ring

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Topological rings and modules (13J99) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)