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A weak-star rational approximation problem connected with subnormal operators

Author: James Dudziak
Journal: Proc. Amer. Math. Soc. 107 (1989), 679-686
MSC: Primary 30E10; Secondary 30H05, 41A65, 47B20
MathSciNet review: 1017226
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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.

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Article copyright: © Copyright 1989 American Mathematical Society