AbstractThis paper investigates the two‐sided uniformly closed ideals of the maximal Op*‐algebraL+(D) of (bounded or unbounded) operators on a dense domainDin a HILBERT space. It is assumed thatDis a FRECHET space with respect to the graph topology. The set of all non‐trivial two‐sided closed ideals ofL+(D) is well‐ordered by inclusion and the α‐th closed ideal
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