Commuting operator solutions of algebraic equations
HTML articles powered by AMS MathViewer
- by R. C. Riddell and R. B. Insley PDF
- Proc. Amer. Math. Soc. 28 (1971), 461-463 Request permission
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
- Nelson Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321–354. MR 63563
- S. R. Foguel, Algebraic functions of normal operators, Israel J. Math. 6 (1968), 199–201. MR 233227, DOI 10.1007/BF02760251
Additional Information
- © Copyright 1971 American Mathematical Society
- 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