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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
DOI: https://doi.org/10.1090/S0002-9939-1971-0276811-4
MathSciNet review: 0276811
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. MR 16, 142. MR 0063563 (16:142d)
  • [2] S. R. Foguel, Algebraic functions of normal operators, Israel J. Math. 6 (1968), 199-201. MR 38 #1550. MR 0233227 (38:1550)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276811-4
Keywords: Scalar-type operator, algebraic operator equation
Article copyright: © Copyright 1971 American Mathematical Society

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