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1978•Canadian Mathematical BulletinOpen access

On the Convergence Vector Space ℒ,(E, F) and its Dual Space

Ronald Beattie

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Abstract

Let E be a locally convex tvs, F a normed space and the space of continuous linear mappings from E into F In this paper, we investigate the continuous convergence structure (c-structure) on. denotes the resulting convergence vector space (cvs). The c-structure is by definition the coarsest cvs structure on making evaluation a continuous mapping.

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What this paper is about

Let E be a locally convex tvs, F a normed space and the space of continuous linear mappings from E into F In this paper, we investigate the continuous convergence structure (c-structure) on. denotes the resulting convergence vector space (cvs). The c-structure is by definition the coarsest cvs structure on making evaluation a continuous mapping.

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Available abstract

Let E be a locally convex tvs, F a normed space and the space of continuous linear mappings from E into F In this paper, we investigate the continuous convergence structure (c-structure) on. denotes the resulting convergence vector space (cvs). The c-structure is by definition the coarsest cvs structure on making evaluation a continuous mapping.

Key concepts: Normed vector space, Mathematics, Dual space, Space (punctuation), Convergence (economics), Locally convex topological vector space, Reflexive space, Dual (grammatical number)

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