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Consider Hankel operators Hφ and H Ψ on the unit sphere in C". If n = 1, then a necessary condition for H* φ H ψ to be compact is lim|z|↑1 ∥Hφkz∥∥Hψkz∥ = 0. We show that when n > 2, this condition is no longer necessary for H* φ H ψ to be compact.

On the compactness of the product of Hankel operators on the sphere