Titlebook: A Course on Topological Vector Spaces; Jürgen Voigt Textbook 2020 Springer Nature Switzerland AG 2020 topology.convex spaces.polars.bipola

濃縮

The Reading Diaries: Four Case StudiesLocally convex spaces are introduced as topological vector spaces possessing a neighbourhood base of zero consisting of convex sets. It is shown that then the topology can also be defined by a set of semi-norms. In order to show this and other features, we first treat separation properties.

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抵押貸款

Cara Lynn Scheuer,Albert J. MillsWe start by discussing semi-reflexivity and Montel spaces and present a number of examples of function spaces. At the end we present duality properties for reflexive spaces and Montel spaces.

失眠癥

特別容易碎

Hanna Salminen,Monika von BonsdorffThis chapter is a short survey on the technical properties mentioned in the title, for subsets of topological vector spaces and locally convex spaces.

前奏曲

Hanna Salminen,Monika von BonsdorffIn this and the following two chapters we discuss some surprising properties concerning the weak topology of Banach spaces. (However, the discussion will not be restricted to Banach spaces!)

欲望

Belinda Yuen,?pela Mo?nik,Winston YapAnother surprising result is Krein’s theorem, stating that the closed convex hull of a weakly compact set in a Banach space is again weakly compact. This will be shown in a much more general context. For the proof, the Pettis integral of vector-valued functions will be defined and applied.

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擴張

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