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On the Matrices A and f(A)

Published online by Cambridge University Press:  20 November 2018

R. C. Thompson
R. C. Thompson*
Affiliation:
University of California, Santa Barbara
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 581 - 587
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Embry, M.R., Nth roots of operators. Proc. Amer. Math. Soc. 19 (1968) 63–68.Google Scholar
2. Thompson, R. C., Generalization of a well-known result in matrix theory. Proc. Glasgow Math. Association 7 (1965) 29–31.Google Scholar