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Commuting Dilations and Uniform Algebras

Published online by Cambridge University Press:  20 November 2018

Takahiko Nakazi
Takahiko Nakazi*
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan
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Let X be a compact Hausdorff space, let C(X) be the algebra of complex-valued continuous functions on X, and let A be a uniform algebra on X. Fix a nonzero complex homomorphism τ on A and a representing measure m for τ on X. The abstract Hardy space Hp = Hp(m), 1 ≤ p ≤ ∞, determined by A is defined to the closure of Lp = Lp(m) when p is finite and to be the weak*-closure of A in L∞ = L∞(m) p = ∞.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 776 - 789
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Abrahamse, M.B., The Pick interpolation theorem for finitely connected domains, Michigan Math. J. 26 (1979) 195–203.Google Scholar
2. Ahern, P.R. and Clark, D.N., Invariant subspaces and analytic continuation in several variables, J. Math. Mech. 19 (1970) 963–969.Google Scholar
3. Ando, T., On a pair of commutative contractions, Acta Sci. Math., 24 (1(1963) 88–90.Google Scholar
4. Barbey, K. and König, H., Abstract analytic function theory and Hardy algebras, Lecture Notes in Mathematics, 593, Springer-Verlag, Berlin, 1977.Google Scholar
5. Beatrous, K. and Burbea, J., Reproducing kernels and interpolation of holomorphic functions , Complex Analysis, Functional Analysis and Approximation Theory, J.Mujica (Ed.), (1986) 25–16.Google Scholar
6. Douglas, R.G. and Paulsen, V.I., Completely bounded maps and hypo-Dirichlet algebras, Acta Sci. Math., 50 (1986), 143–157.Google Scholar
7. Gamelin, T., Uniform Algebras,2nd éd., Chelsea, New York, (1984).Google Scholar
8. Koranyi, G. and Pukánski, A., Holomorphic functions with positive real part on polycyylinders, Trans. Amer. Math. Soc. 108 (1983) 449–456.Google Scholar
9. Sz-Nagy, B. and Foiaş, C., Dilation des commutants d'opérateurs, C.R. Acad. Sci. Paris Sér. A-B 266 (1968)493–495.Google Scholar
10. Nakazi, T., Norms ofHankel operators and uniform algebras, Trans. Amer. Math. Soc. 299 (1987) 573–580.Google Scholar
11. Nakazi, T., Norms ofHankel operators and uniform algebras, II, Tohoku Math. J. 39 (1987) 543- 555.Google Scholar
12. Nakazi, T. and Yamamoto, T., A lifting theorem and uniform algebras, Trans. Amer. Math. Soc. 305 (1988)79–94.Google Scholar
13. Parrott, S., Unitary dilations for commuting contractions, Pacific J. Math., 34 (1973) 481–490.Google Scholar
14. Sarason, D., Generalized interpolation in H∞ , Trans. Amer. Math. Soc. 127 (1967) 179–203.Google Scholar
15. Varopoulos, N. Th., On an inequality of von Neumann and application of the metric theory of tensorproducts to operators theory, J. Funct. Anal. 16 (1974) 83–100.Google Scholar
16. Suciu, I., Function Algebras , translated from the Romanian by Mihailescu, M., Editura Academiei Republicii Socialiste Romania, Bucuresti (1973).Google Scholar