| Abstract: | This paper investigates the two-sided uniformly closed ideals of the maximal Op*-algebra L+(D) of (bounded or unbounded) operators on a dense domain D in a HILBERT space. It is assumed that D is a FRECHET space with respect to the graph topology. The set of all non-trivial two-sided closed ideals of L+(D) is well-ordered by inclusion and the α-th closed ideal ??α is generated by the orthogonal projections onto HILBERTian subspaces of D of dimension less then ??α. An element A in L+(D) belongs to the minimal closed ideal ??0 if and only if the following two equivalent conditions are satisfied: a) A maps bounded subsets of D into relatively compact sets. b) A maps weakly convergent sequences in D into convergent sequences. |
