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The Nevanlinna-Pick theorem and a non-positive definite matrix

Published online by Cambridge University Press:  17 April 2009

Takahiko Nakazi
Takahiko Nakazi
Affiliation:
Department of Mathematics Faculty of Science (General Education), Hokkaido University, Sapporo 060, Japan
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Let {zj} be an interpolation sequence in the open unit disc and {wj} a bounded sequence. In this note, it is shown that there is a function F in H∞ + C satisfying ‖F‖ ≤ 1 and as j → ∞ if and only if there exists a compact matrix [tij] such that on where .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 361 - 365
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Axler, S., Berg, I.D., Jewell, N., and Shields, A., “Approximation by compact operators and the space H ∞ + C“, Ann. of Math., 109 (1979), 601–612.CrossRefGoogle Scholar
[2]Clark, D.N., “On interpolating sequences and the theory of Hankel and Toeplitz matrices”, J. Funct. Anal. 5 (1970), 247–258.CrossRefGoogle Scholar
[3]Guillory, C., Izuchi, K. and Sarason, D., “Interpolating Blaschke products and division in Douglas algebras”, Proc. Roy. Irish Acad. Sect. A, 84 (1984), 1–7.Google Scholar
[4]Sarason, D., “Generalized interpolation in H ∞“, Trans. Amer. Math. Soc., 127 (1967), 179–203.Google Scholar