On the Topology of the Space of Hankel Convolution Operators

AbstractLet Hμbe the Zemanian space of Hankel transformable functions, let O′μ,#be its space of convolution operators, and let Oμ,#be the predual of O′μ,#. We prove that the topology of uniform convergence on bounded subsets of Hμand the strong dual toplogy coincide on O′μ,#. 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 Oμ,#being reflexive, complete, nuclear, and Montel are established