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Título:
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Locally determining sequences in infinite-dimensional spaces.
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Autores:
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Ansemil, José María M. ;
Dineen, Seán
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Tipo de documento:
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texto impreso
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Editorial:
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Università del Salento, 1987
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Ecuaciones diferenciales
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Tipo = Artículo
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Resumen:
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A subset L of a complex locally convex space E is said to be locally determining at 0 for holomorphic functions if for every connected open 0-neighborhood U and every f?H(U), whenever f vanishes on U?L, then f?0. The authors' main result is that if E is separable and metrizable, then every set which is locally determining at 0 contains a null sequence which is also locally determining at 0. This answers a question of J. Chmielowski [Studia Math. 57 (1976), no. 2, 141–146;], who was the first to study locally determining sets. The proof of the main theorem makes use of the following result of K. F. Ng [Math. Scand. 29 (1971), 279–280;]: Let E be a normed space with closed unit ball BE. Suppose that there is a Hausdorff locally convex topology ? on E such that (BE,?) is compact. Then E with its original norm is the dual of the normed space F={??E?: ?|BE is ?-continuous}, with norm ???=sup{|?(x)|: x?BE}
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En línea:
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https://eprints.ucm.es/id/eprint/22543/1/Ansemil20.pdf
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