کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9503074 | 1339554 | 2005 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Group duality with the topology of precompact convergence
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The Pontryagin-van Kampen (P-vK) duality, defined for topological Abelian groups, is given in terms of the compact-open topology. Polar reflexive spaces, introduced by Köthe, are those locally convex spaces satisfying duality when the dual space is equipped with the precompact-open topology. It is known that the additive groups of polar reflexive spaces satisfy P-vK duality. In this note we consider the duality of topological Abelian groups when the topology of the dual is the precompact-open topology. We characterize the precompact reflexive groups, i.e., topological groups satisfying the group duality defined in terms of the precompact-open topology. As a consequence, we obtain a new characterization of polar reflexive spaces. We also present an example of a space which satisfies P-vK duality and is not polar reflexive. Some of our results respond to questions appearing in the literature.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 303, Issue 1, 1 March 2005, Pages 274-287
Journal: Journal of Mathematical Analysis and Applications - Volume 303, Issue 1, 1 March 2005, Pages 274-287
نویسندگان
Salvador Hernández, F. Javier Trigos-Arrieta,