Duality

R. Beattie and H.-P. Butzmann
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R. Beattie: Mount Allison University, Department of Mathematics and Computer Science
H.-P. Butzmann: Universität Mannheim, Fakultät für Mathematik und Informatik

Chapter Chapter 4 in Convergence Structures and Applications to Functional Analysis, 2002, pp 119-152 from Springer

Abstract: Abstract If E is a Hausdorff locally convex topological vector space, then there is no vector space topology on 𝓛E making the evaluation ω e : 𝓛E x E → 𝕂 continuous unless E is a normed space. This is a very serious shortcoming and was one of the main motivations for the study of convergence structures. Clearly the continuous convergence structure on 𝓛E makes evaluation continuous for every convergence vector space E. The resulting space 𝓛 c E is called the dual space of E. We sometimes also call it the continuous dual or c-dual of E in order to distinguish it from the strong dual of a locally convex topological vector space or the normed dual of a normed space.

Keywords: Vector Space; Closed Subspace; Topological Vector Space; Inductive Limit; Projective Limit (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-015-9942-9_4

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