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Linearization of holomorphic mappings on fully nuclear spaces with a basis

Published online by Cambridge University Press:  18 May 2009

Seán Dineen ,
Pablo Galindo ,
Domingo García  and
Manuel Maestre
Seán Dineen
Affiliation:
Department of Mathematics, University College, Dublin, Dublin 4, Ireland
Pablo Galindo
Affiliation:
Department de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjasot (Valencia), Spain
Domingo García
Affiliation:
Department de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjasot (Valencia), Spain
Manuel Maestre
Affiliation:
Department de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjasot (Valencia), Spain
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In [13] Mazet proved the following result.

If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;

The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 2 , May 1994 , pp. 201 - 208
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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