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Reductivity in<i>C</i><sup>โˆ—</sup>-algebras and essentially reductive operators

Reductivity in<i>C</i><sup>โˆ—</sup>-algebras and essentially reductive operators

Reductivity is defined in the context of C*-algebras other than the algebra of bounded operators on Hubert space, and several examples are given.Essentially reductive operators are defined as operators whose images are reductive in the Calkin algebra.It is shown that every essentially reductive operator must be a compact perturbation of โ€ฆ