Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T21:26:18.059Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpolation problem for l1 and a uniform algebra

Part of: Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  09 April 2009

Takahiko Nakazi
Takahiko Nakazi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let A be a uniform algebra and M(A) the maximal ideal space of A. A sequence {an} in M(A) is called l1-interpolating if for every sequence (αn) in l1 there exists a function f in A such that f (an) = αn for all n. In this paper, an l1-interpolating sequence is studied for an arbitrary uniform algebra. For some special uniform algebras, an l1-interpolating sequence is equivalent to a familiar l-interpolating sequence. However, in general these two interpolating sequences may be different from each other.

Keywords

uniform algebrallnterpolationmaximal ideal spacepseudo-hyperbolic distance

MSC classification

Secondary: 46J10: Banach algebras of continuous functions, function algebras 46J15: Banach algebras of differentiable or analytic functions, $H^p$-spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 1 - 12
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Berndtsson, B., Chang, S.-Y. A. and Lin, K.-C., ‘Interpolating sequences in the polydisc’, Trans. Amer. Math. Soc. (1) 302 (1987), 161–169.CrossRefGoogle Scholar
[2]Carleson, L., ‘An interpolation problem for bounded analytic functions’, Amer. J. Math. 80 (1958), 921–930.CrossRefGoogle Scholar
[3]Hatori, O., ‘The Shapiro-Shields theorem on finite connected domains’, Sūrikaisekikenkyūsho Kōkyūroku 1049 (1998), 21–29 (in Japanese).Google Scholar
[4]Izuchi, K., ‘Interpolating sequences in the maximal ideal space of H∞ II’, in: Operator theory and complex analysis (Sapporo, 1991) (Birkhäuser, Basel, 1992) pp. 221–233.CrossRefGoogle Scholar
[5]Izuchi, K. and Izuchi, Y., ‘Algebras of bounded analytic functions containing the disk algebra’, Canad. J. Math. 38 (1986), 87–108.CrossRefGoogle Scholar
[6]Narita, J., ‘Interpolating sequences on plane domains’, Kodai Math. J. 13 (1990), 311–316.CrossRefGoogle Scholar
[7]Shapiro, H. S. and Shields, A. L., ‘On some interpolation problems for analytic functions’, Amer. J. Math. 83 (1961), 513–532.CrossRefGoogle Scholar
[8]Stout, E. L., ‘Bounded holomorphic functions on finite Reimann surfaces’, Trans. Amer. Math. Soc. 120 (1965), 255–285.Google Scholar
[9]Zalcman, L., ‘Bounded analytic functions on domains of infinite connectivity’, Trans. Amer. Math. Soc. 144 (1969), 241–269.CrossRefGoogle Scholar