Corona problem with data in ideal spaces of sequences

Original · EN

Let E be a Banach lattice on Z having order continuous norm. We show that for any function f = {fⱼ}ⱼ ∈ Z from the Hardy space H∞ (E) such that δ f (z)ₑ 1 for all z from the unit disk D there exists some solution g = {gⱼ}ⱼ ∈ Z ∈ H∞ (E'), gₕ∞ ₍ₑ'₎ Cδ of the Bézout equation ∑ⱼ fⱼ gⱼ = 1, also known as the vector-valued corona problem with data in H∞ (E).