A theorem on reproducing kernel hilbert spaces of pairs

In this paper we study reproducing kernel Hilbert and Banacli spaces of pairs. These are a generalization of reproducing kernel Hilbert spaces and, roughly speaking, consist of pairs of Hilbert (or Banaeh) spaces of functions in duality with respect to a sesquilinear form and admitting a left and a right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z,w) analytic in z and w* there is a neighborhood of the origin that can be associated with a reproducing kernel Hilbert space of pairs with left reproducing kernel K(z,w) and right reproducing kernel K(w, z)*.