Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1989-1017226-4
MathSciNet review: 1017226
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30E10, 30H05, 41A65, 47B20

Retrieve articles in all journals with MSC: 30E10, 30H05, 41A65, 47B20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-1017226-4
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society