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arXiv · 2508.11123

On Banach spaces with angelic Mackey duals

Douglas Mupasiri
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Abstract

We show that if $X$ is a sequentially reflexive Banach space, then its Mackey dual $(X^{*},τ(X^{*}, X))$ is an angelic space. This builds on a result of J. Howard which says that in the Mackey dual $(X^{*}, τ(X^{*}, X))$ of a Banach space $X$, relative sequential compactness is, in general, strictly stronger than relative compactness and that the two notions of compactness are equivalent if $X$ is reflexive or separable. Our main result gives a characterization of the sequentially reflexive spaces as the Banach spaces $X$ for which the the finest locally convex topology on $X^{*}$ with the same precompact sets as the Mackey topology $τ(X^{*}, X)$ is the bound extension of $τ(X^{*}, X)$.

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Douglas Mupasiri. 2025-08-15. On Banach spaces with angelic Mackey duals. https://arxiv.org/abs/2508.11123

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