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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Interpolating sequences for bounded analytic functions


Authors: Pablo Galindo and Alejandro Miralles
Journal: Proc. Amer. Math. Soc. 135 (2007), 3225-3231
MSC (2000): Primary 46G20; Secondary 32A65
Published electronically: May 14, 2007
MathSciNet review: 2322753
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Abstract: We prove that any sequence in the open ball of a complex Banach space $ E,$ even in that of $ E^{**},$ whose norms are an interpolating sequence for $ H^\infty,$ is interpolating for the space of all bounded analytic functions on $ B_E.$ The construction made yields that the interpolating functions depend linearly on the interpolated values.


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Additional Information

Pablo Galindo
Affiliation: Departamento de Análisis Matemático, Dr. Moliner, 50, Burjassot 46100, Universidad de Valencia, Spain
Email: Pablo.Galindo@uv.es

Alejandro Miralles
Affiliation: Departamento de Análisis Matemático, Dr. Moliner, 50, Burjassot 46100, Universidad de Valencia, Spain
Email: Alejandro.Miralles@uv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08863-6
PII: S 0002-9939(07)08863-6
Keywords: Analytic function, Banach space, interpolation
Received by editor(s): June 21, 2006
Published electronically: May 14, 2007
Additional Notes: Supported by MEC and FEDER Project BFM 2003-07540 (DGI. Spain)
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society