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ASYMPTOTIC INTERPOLATING SEQUENCES IN UNIFORM ALGEBRAS

Published online by Cambridge University Press:  24 March 2003

PAMELA GORKIN  and
RAYMOND MORTINI
PAMELA GORKIN
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania, PA 17837, [email protected]
RAYMOND MORTINI
Affiliation:
Départment de Mathématiques, Université de Metz, Ile du Saulcy, F-57045 Metz, [email protected]
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Abstract

T. Hosokawa, K. Izuchi and D. Zheng recently introduced the concept of asymptotic interpolating sequences (of type 1) in the unit disk for $H^\infty$(${\bb D}$). It is shown that these sequences coincide with sequences that are interpolating for the algebra $QA$. Also a characterization is given of the interpolating sequences of type $1$ for $H^\infty$(${\bb D}$), and asymptotic interpolating sequences in the spectrum of $H^\infty$(${\bb D}$) are studied. The existence of asymptotic interpolating sequences of type $1$ for $H^\infty(\Omega)$ on arbitrary domains is verified. It is shown that any asymptotic interpolating sequence in a uniform algebra eventually is interpolating.

Keywords

46J15
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 481 - 498
Copyright
The London Mathematical Society 2003

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Footnotes

This research was supported by the RIP-programme Oberwolfach, 2001.