For a class of essentially normal operators, we characterize their norm closures of (U + K)-orbits. Moreover, we introduce a notion of the quasiapproximate (U + K)-equivalence of essentially normal operators and determine completely the quasiapproximate (U + K)-invariants. Finally, we give the canonical forms of essentially normal operators under this quasiapproximate (U + K)-equivalence. (2000). Primary 47A10; Secondary 47A55.
Mathematics Subject Classification
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