LOCALIZED STRICT TOPOLOGIES ON MULTIPLIER ALGEBRAS OF PRO-C∗-ALGEBRAS

The bounded localization β_b of a locally convex topology β is defined as the finest locally convex topology agreeing with β on all bounded sets. We show that the strict topology on the multiplier algebra of a bornological pro-C∗-algebra equals its own localization, generalizing the analogous result due to Taylor for multiplier algebras of plain C∗-algebras. We also (a) characterize the barreled commutative unital pro-C∗-algebras as those of continuous functions on functionally Hausdorff spaces whose relatively pseudocompact subsets are relatively compact, equipped with the topology of uniform convergence on compact subsets, and (b) describe a contravariant equivalence between the category of commutative unital pro-C∗-algebras and a category of Tychonoff (rather than functionally Hausdorff) topological spaces.