Bounded elements of C*-inductive locally convex spaces

摘要

The notion of bounded element of C*-inductive locally convex spaces (orC*-inductive partial *-algebras) is introduced and discussed in two ways: thefirst one takes into account the inductive structure provided by certainfamilies of C*-algebras; the second one is linked to natural order of thesespaces. A particular attention is devoted to the relevant instance provided bythe space of continuous linear maps acting in a rigged Hilbert space.