Geodesic
On the Matrices A and f(A)
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 581-587

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In a recent note [1], M. R. Embry proved that if A is an operator on a Banach space then, under a certain condition on the spectrum of A, each operator commuting with An also commutes with A, where n is a fixed positive integer. It turns out that, when A is a finite matrix, Embry′s conditions imply that A is a polynomial in An and hence plainly each operator commuting with An also commutes with A. 
Thompson, R. C. On the Matrices A and f(A). Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 581-587. doi: 10.4153/CMB-1969-075-7
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[1] 1. Embry, M.R., Nth roots of operators. Proc. Amer. Math. Soc. 19 (1968) 63–68. Google Scholar

[2] 2. Thompson, R. C., Generalization of a well-known result in matrix theory. Proc. Glasgow Math. Association 7 (1965) 29–31. Google Scholar

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