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Ansemil, José María M. and Dineen, Seán (1987) Locally determining sequences in infinitedimensional spaces. Note di Matematica, 7 (1). pp. 4145. ISSN 11232536

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Official URL: http://sibaese.unisalento.it/index.php/notemat/article/view/1591/1371
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http://sibaese.unisalento.it/index.php/index/index  Publisher 
Abstract
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 0neighborhood 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 τ on E such that (BE,τ) is compact. Then E with its original norm is the dual of the normed space F={φ∈E∗: φBE is τcontinuous}, with norm ∥φ∥=sup{φ(x): x∈BE}
Item Type:  Article 

Uncontrolled Keywords:  identity theorem; locally determining at zero for holomorphic functions; separable metrizable locally convex space; null sequence 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  22543 
Deposited On:  24 Jul 2013 11:15 
Last Modified:  10 Aug 2018 08:56 
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