A counterexample to the corona theorem for operators on H²(𝔻ⁿ)

E. Amar and C. Menini

Vol. 206 (2002), No. 2, 257–269

DOI: 10.2140/pjm.2002.206.257

Abstract

We built a counterexample to the corona theorem for operators in H^∞(ℒ(H²(𝔻ⁿ⁻¹)) for n ≥ 4, which is close to a counterexample to the corona theorem for functions in the sense that the associated subspaces are invariant by all the shifts.

Milestones

Received: 8 May 2000

Revised: 1 February 2002

Published: 1 October 2002