On the distinguished character of the function spaces of holomorphic mappings of bounded type |
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Authors: | JM Isidro |
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Institution: | Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Santiago de Compostela, Spain |
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Abstract: | Given two complex normed spaces E and F, F complete, and a balanced open subset U of E, we prove that the space (b(U, F) of the holomorphic mappings f: U → F of bounded type, endowed with its natural topology τb, is a distinguished quasi-normable Fréchet space, which is not a Schwartz space unless dim E < ∞ and dim F < ∞. |
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