Quaternionic Hankel operators and approximation by slice regular functions

In this paper, we study Hankel operators in the quaternionic setting. In particular, we prove that they can be exploited to measure the L^infty distance of a slice L^infty function (i.e., an essentially bounded function on the quaternionic unit sphere that is affine with respect to quaternionic imaginary units) from the space of bounded slice regular functions (i.e., bounded quaternionic power series on the quaternionic unit ball). Among the difficulties arising from the non-commutative context, there is the lack of a good factorization result for slice regular functions in the Hardy space H^1