For a large family of operators in B(H), the irreducible operators are dense with respect to the trace-class norm.
Normed ideal perturbation of irreducible operators in semifinite von Neumann factors.Integral Equations Operator Theory93(2021), no
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Density of irreducible operators in the trace-class norm
For a large family of operators in B(H), the irreducible operators are dense with respect to the trace-class norm.