The Quasiapproximate $(\mathcal{U} + \mathcal{K})$ ?Invariants of Essentially Normal Operators

Abstract

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