ON THE TOPOLOGY OF THE SPACE OF HANKEL CONVOLUTION OPERATORS

摘要

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 be the predual of O-mu,O-#'. We prove that the topology of uniform convergence on bounded subsets of H-mu and the strong dual toplogy coincide on O-mu,O-#'. Our technique, involving Mackey topologies, differs from, and is simpler than, those usually employed with the same purpose for other spaces of convolution operators, to which it is also applicable. As a consequence, the properties of O-mu,O-# being reflexive, complete, nuclear, and Montel are established. (C) 1996 Academic Press, Inc. [References: 18]