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 be a positive Borel measure on a compact subset of the complex plane. Denote the weak-star closure in of by . Given , denote the weak-star closure in of the algebra generated by and the complex conjugate of by . This paper determines the structure of . As a consequence, a solution is obtained to a problem concerned with minimal normal extensions of functions of a subnormal operator.

**[AK]**M. B. Abrahamse and Thomas L. Kriete,*The spectral multiplicity of a multiplication operator*, Indiana Univ. Math. J.**22**(1972/73), 845–857. MR**0320797****[Ch]**J. Chaumat,*Adherence faible étoile d'algebres de fractions rationelles*, Publications Mathématique d'Orsay, No. 147.**[C]**John B. Conway,*The minimal normal extension of a function of a subnormal operator*, Analysis at Urbana, Vol. II (Urbana, IL, 1986–1987) London Math. Soc. Lecture Note Ser., vol. 138, Cambridge Univ. Press, Cambridge, 1989, pp. 128–140. MR**1009188****[CO]**J. B. Conway and R. F. Olin,*A functional calculus for subnormal operators*, II, Memoirs Amer. Math. Soc. No. 184, Providence, R.I.**[D]**James Dudziak,*The minimal normal extension problem for subnormal operators*, J. Funct. Anal.**65**(1986), no. 3, 314–338. MR**826430**, 10.1016/0022-1236(86)90022-4**[G1]**Theodore W. Gamelin,*Uniform algebras*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR**0410387****[G2]**-,*Rational approximation theory*, Univ. California at Los Angeles Lecture Notes (unpublished), Los Angeles, CA.**[GRT]**T. W. Gamelin, P. Russo, and J. E. Thomson,*A Stone-Weierstrass theorem for weak-star approximation by rational functions*, J. Funct. Anal.**87**(1989), no. 1, 170–176. MR**1025885**, 10.1016/0022-1236(89)90006-2

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DOI:
https://doi.org/10.1090/S0002-9939-1989-1017226-4

Article copyright:
© Copyright 1989
American Mathematical Society