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On the Matrices A and f(A)
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1969
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