ON THE TOPOLOGY OF THE SPACE OF HANKEL CONVOLUTION-OPERATORS

Let H-mu be the Zemanian space of Hankel transformable functions, let O-mu,O-#' be its space of convolution operators, and let O-mu,O-# if b e the predual of O-mu,O-#'. We prove that the topology of uniform conv ergence on bounded subsets of H-mu and the strong dual toplogy coincid e on O-mu,O-#'. Our technique, involving Mackey topologies, differs fr om, and is simpler than, those usually employed with the same purpose for other spaces of convolution operators, to which it is also applica ble. As a consequence, the properties of O-mu,O-# being reflexive, com plete, nuclear, and Montel are established. (C) 1996 Academic Press, I nc.