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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commuting operator solutions of algebraic equations


Authors: R. C. Riddell and R. B. Insley
Journal: Proc. Amer. Math. Soc. 28 (1971), 461-463
MSC: Primary 47.30
MathSciNet review: 0276811
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Abstract: Let $ G(w,z)$ be a complex polynomial, and $ S$ a bounded operator of scalar type on a complex Banach space, whose spectrum avoids the points $ \lambda $ for which $ G(\lambda ,z) = 0$ has multiple roots $ z$. The form of a bounded operator $ T$ which commutes with $ S$ and satisfies $ G(S,T) = 0$ is established.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0276811-4
PII: S 0002-9939(1971)0276811-4
Keywords: Scalar-type operator, algebraic operator equation
Article copyright: © Copyright 1971 American Mathematical Society