Abstract :
Let H be the Zemanian space of Hankel transformable functions, let OX be m m, a
its space of convolution operators, and let O be the predual of OX . We prove m, a m, a
that the topology of uniform convergence on bounded subsets of H and the strong m
dual toplogy coincide on OX . Our technique, involving Mackey topologies, differs m, a
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 being reflexive, complete, nuclear, and Montel are estab- m, a
lished. Q
