  In previous work, we defined and studied $\Sigma^*$-modules, a class of
Hilbert $C^*$-modules over $\Sigma^*$-algebras (the latter are $C^*$-algebras
that are sequentially closed in the weak operator topology). The present work
continues this study by developing the appropriate $\Sigma^*$-algebraic
analogue of the notion of strong Morita equivalence for $C^*$-algebras. We
define strong $\Sigma^*$-Morita equivalence, prove a few characterizations,
look at the relationship with equivalence of categories of a certain type of
Hilbert space representation, study $\Sigma^*$-versions of the interior and
exterior tensor products, and prove a $\Sigma^*$-version of the
Brown-Green-Rieffel stable isomorphism theorem.
