On a minimal normal dilation problem
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- Proc. Amer. Math. Soc. 121 (1994), 843-850 Request permission
Abstract:
By combining the theory of disintegration of measures with certain approximation theorems in several complex variables, we derive some positive results concerning a minimal normal dilation problem for operator tuples whose coordinates are special functions of subnormal operators as well as their adjoints.References
-
N. Bourbaki, Èléments des mathématique, Livre VI, Intégration, Chapitre 6, Intégration Vectorielle, Hermann, Paris, 1959.
- 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
- John B. Conway, Towards a functional calculus for subnormal tuples: the minimal normal extension, Trans. Amer. Math. Soc. 326 (1991), no. 2, 543–567. MR 1005077, DOI 10.1090/S0002-9947-1991-1005077-X
- James Dudziak, The minimal normal extension problem for subnormal operators, J. Funct. Anal. 65 (1986), no. 3, 314–338. MR 826430, DOI 10.1016/0022-1236(86)90022-4
- L. Hörmander and J. Wermer, Uniform approximation on compact sets in $C^{n}$, Math. Scand. 23 (1968), 5–21 (1969). MR 254275, DOI 10.7146/math.scand.a-10893
- Takasi Itô, On the commutative family of subnormal operators, J. Fac. Sci. Hokkaido Univ. Ser. I 14 (1958), 1–15. MR 0107177
- Gerald M. Leibowitz, Lectures on complex function algebras, Scott, Foresman & Co., Glenview, Ill., 1970. MR 0428042 A. G. O’Farrell and K. J. Preskenis, Approximation by polynomials in two complex variables, Math. Ann. 246 (1980), 225-232.
- Kenneth John Preskenis, Another view of the Weierstrass theorem, Proc. Amer. Math. Soc. 54 (1976), 109–113. MR 390779, DOI 10.1090/S0002-9939-1976-0390779-6
- Kenneth John Preskenis, Approximation by polynomials in $z$ and another function, Proc. Amer. Math. Soc. 68 (1978), no. 1, 69–74. MR 457740, DOI 10.1090/S0002-9939-1978-0457740-6
- Mihai Putinar, Spectral inclusion for subnormal $n$-tuples, Proc. Amer. Math. Soc. 90 (1984), no. 3, 405–406. MR 728357, DOI 10.1090/S0002-9939-1984-0728357-3
- J. Wermer, Approximation on a disk, Math. Ann. 155 (1964), 331–333. MR 165386, DOI 10.1007/BF01354865
- John Wermer, Banach algebras and several complex variables, 2nd ed., Graduate Texts in Mathematics, No. 35, Springer-Verlag, New York-Heidelberg, 1976. MR 0394218
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 843-850
- MSC: Primary 47A20; Secondary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186126-3
- MathSciNet review: 1186126