Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-22T03:44:33.020Z Has data issue: false hasContentIssue false

Interpolating sequence on certain Banach spaces of analytic functions

Published online by Cambridge University Press:  17 April 2009

B. Yousefi
Affiliation:
Deparement of Mathematics, Shiraz University, Shiraz 71454, Iran 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 G be a finitely connected domain and let X be a reflexive Banach space of functions analytic on G which admits the multiplication Mz as a polynomially bounded operator. We give some conditions that a sequence in G has an interpolating subsequence for X.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Axler, S., ‘Interpolation by multipliers of the Dirichlet space’, Quart. J. Math. Oxford 43 (1992), 409419.CrossRefGoogle Scholar
[2]Chan, K.C., ‘On the Dirichlet space for finitely connected regions’, Trans. Amer. Math. Soc. 319 (1990), 711728.CrossRefGoogle Scholar
[3]Chan, K.C. and Shields, A.L., ‘Zero sets, interpolating sequences, and cyclic vectors for Dirichlet spaces’, Michigan Math. J 39 (1992), 289307.CrossRefGoogle Scholar
[4]Dor, L.E., ‘On sequences spanning a complex ℓ1 space’, Proc. Amer. Math. Soc. 47 (1975), 515516.Google Scholar
[5]Gamelin, T., Uniform algebras (Chelsea, New York, 1984).Google Scholar
[6]Garnett, J.B., Bounded analytic functions, Pure and Applied Maths. 96 (Academic Press, New York, 1981).Google Scholar
[7]Rosenthal, H.P., ‘A characterization of Banach spaces containing ℓ1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 24112413.CrossRefGoogle Scholar
[8]seddighi, K., Hedayatiyan, K. and Yousefi, B., ‘Operators acting on certain Banach spaces of analytic functions’, Internat. J. Math. Sci. 18 (1995), 107110.CrossRefGoogle Scholar