A weak-star rational approximation problem connected with subnormal operators
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- by James Dudziak PDF
- Proc. Amer. Math. Soc. 107 (1989), 679-686 Request permission
Abstract:
Let $\mu$ be a positive Borel measure on a compact subset $K$ of the complex plane. Denote the weak-star closure in ${L^\infty }\left ( \mu \right )$ of $R\left ( K \right )$ by ${R^\infty }\left ( {K,\mu } \right )$. Given $f \in {R^\infty }\left ( {K,\mu } \right )$, denote the weak-star closure in ${L^\infty }\left ( \mu \right )$ of the algebra generated by ${R^\infty }\left ( {K,\mu } \right )$ and the complex conjugate of $f$ by ${A^\infty }\left ( {f,\mu } \right )$. This paper determines the structure of ${A^\infty }\left ( {f,\mu } \right )$. As a consequence, a solution is obtained to a problem concerned with minimal normal extensions of functions of a subnormal operator.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 679-686
- MSC: Primary 30E10; Secondary 30H05, 41A65, 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1989-1017226-4
- MathSciNet review: 1017226