Reflexive extended locally convex spaces

2023/09/23 by Kumar, Akshay, Jindal, Varun
#46A20 #46A25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2309.13314

Abstract

For an extended locally convex space (elcs) (X,τ), the authors in [10] studied the topology τ_ucb of uniform convergence on bounded subsets of (X,τ) on the dual X^* of (X,τ). In the present paper, we use the topology τ_ucb to explore the reflexive property of extended locally convex spaces. It is shown that an elcs is (semi) reflexive if and only if any of its open subspaces is (semi) reflexive. For an extended normed space, we show that reflexivity is a three-space property.

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