Localized strict topologies on multiplier algebras of pro-C^*-algebras - Chirvasitu, Alexandru (Topology Proceedings, 2024)
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.