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On New Banach Spaces of Analytic Mappings

Cecília S. Fernandez
Mathematical Proceedings of the Royal Irish Academy
Vol. 99A, No. 1 (Sep., 1999), pp. 1-16
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/20459738
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On New Banach Spaces of Analytic Mappings
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Abstract

In infinite dimensional holomorphy most of the spaces encountered in the literature are not Banach spaces. Since there is a large number of Banach spaces of analytic functions in the one complex variable theory, we ask if these spaces can generate, in an interesting and natural way, Banach spaces of analytic functions in any complex Banach space. In this work, we present a method of construction of Banach spaces of analytic functions on the open unit ball of any complex Banach space from Banach spaces of analytic functions in the open unit disk. We also present some properties of these spaces.

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