On the topology of the space of Hankel convolution operators (Q1922976)

The authors consider the topology in the space of Hankel operators. Let \({\mathcal H}_\mu\) be the Zemanian space of Hankel transformable functions [\textit{A. H. Zemanian}, ``Generalized integral transformations'', New York (1968; Zbl 0181.12701)], let \({\mathcal O}_{\mu,\#}'\) be the space of Hankel convolutions acting in \({\mathcal H}_\mu\), and let \({\mathcal O}_{\mu,\#}\) be the predual of \({\mathcal O}_{\mu,\#}'\). The authors prove that the topology of uniform convergence on bounded subsets of \({\mathcal H}_\mu\) and the strong dual topology coincide on \({\mathcal O}_{\mu,\#}'\). As a consequence they established that \({\mathcal O}_{\mu,\#}\) is reflexive, complete, nuclear and Montel.