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We built a counterexample to the corona theorem for operators in H∞(L(H 2 (D n-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.

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

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