College of Mathematics and Information Science, Shangqiu Normal University, Shangqiu, China.
In [Perturbation of Spectrums of 2 × 2 Operator Matrices, Proceedings of the American Mathematical Society, Vol. 121, 1994], the authors asked whether there was an operator 
such that 
for a given pair (A,B) of operators, where the operator 
was defined by 
. In this note, a partial answer for the question is given.
H. Zhang, "Spectra of 2 × 2 Upper-Triangular Operator Matrices," Applied Mathematics, Vol. 4 No. 11, 2013, pp. 22-25. doi: 10.4236/am.2013.411A1004.
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http://dx.doi.org/10.1007/978-1-4757-3828-5