| 书目名称 | Functional Analysis in Asymmetric Normed Spaces | | 编辑 | Ştefan Cobzaş | | 视频video | | | 概述 | First treatment in book form of basic results on asymmetric normed spaces The presentation follows the ideas from the theory of normed spaces, emphasizing similarities as well as differences with resp | | 丛书名称 | Frontiers in Mathematics | | 图书封面 |  | | 描述 | An asymmetric norm is a positive definite sublinear functional .p. on a real vector space .X.. The topology generated by the asymmetric norm .p. is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of .X., meaning the set of all real-valued upper semi-continuous linear functionals on .X., is merely a convex cone in the vector space of all linear functionals on .X.. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped | | 出版日期 | Book 2013 | | 关键词 | asymmetric norm; bitopological space; quasi-metric space; quasi-uniform space | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-0478-3 | | isbn_softcover | 978-3-0348-0477-6 | | isbn_ebook | 978-3-0348-0478-3Series ISSN 1660-8046 Series E-ISSN 1660-8054 | | issn_series | 1660-8046 | | copyright | Springer Basel 2013 |
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发表于 2025-3-21 18:19:03
