Some problems on 𝐵-completeness

Mukherjee, T. K.

doi:10.1090/S0002-9939-1974-0367613-1

Some problems on $B$-completeness
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Proc. Amer. Math. Soc. 46 (1974), 367-374 Request permission

Abstract:

In this paper, we give examples to show the following: 1. The product of two $B$-complete spaces is not necessarily ${B_r}$-complete. 2. The Mackey dual of a strict LF-space is not necessarily ${B_r}$-complete. 3. A separable, reflexive, and strict LF-space is not, in general, ${B_r}$-complete. The second point has reference to a problem of Dieudonné and Schwartz which asks essentially whether the Mackey dual of a strict LF-space is $B$-complete and which was answered in the negative by Grothendieck.

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