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May 11 at 18:22 comment added Bill Johnson Yes, it is elementary that a Fréchet space $X$ is a BK space if and only if there is a continuous linear injection from $X$ into $\mathbb C^{\mathbb N}$ (with the product topology) if and only if $X^*$ is weak$^*$ separable.
May 9 at 10:04 history answered Jochen Wengenroth CC BY-SA 4.0