Triangular Truncation and Normal Limits of Nilpotent Operators
Don Hadwin · Proceedings of the American Mathematical Society · 1995
We show that, as $n \to \infty$, the product of the norm of the triangular truncation map on the $n \times n$ complex matrices with the distance from the norm-one hermitian $n \times n$ matrices to the nilpotents converges to 1/2. We also include an elementary proof of D. Herrero’s characterization of the normal operators that are norm limits of nilpotents.