Locally Convex Spaces with the B(φ)-Property

Taqdir Husain
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Taqdir Husain: McMaster University

Chapter 7 in The Open Mapping and Closed Graph Theorems in Topological Vector Spaces, 1965, pp 82-95 from Springer

Abstract: Abstract Comparing the different notions of hypercomplete, B-complete, B r -complete, and complete 1.c. spaces E dealt with in the preceding chapters, one observes that each of these notions depends upon the coincidence of the ew*-topology with the a(E′, E)-topology on some prescribed sets of the dual E′ of E. More precisely, let Q be an arbitrary set of the dual E′ of an 1.c. space E and suppose the following statement is true: (A′) Q is σ(E′, E)-closed if and only if it is ew*-closed.

Keywords: Banach Space; Identity Mapping; Open Mapping; Norm Topology; Dense Subspace (search for similar items in EconPapers)
Date: 1965
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DOI: 10.1007/978-3-322-96210-2_7

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