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When I read an article recently, I see this statement as a conjecture.
So I want to ask, do all nuclear Frechet space have Schauder basis?
Is this still open? Or has been solved? I’ll appreciate any comments or references you give. Thanks a lot.

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    $\begingroup$ The answer to the question in your title is negative (Mitiagin, Zobin, 1974). $\endgroup$
    – ifatfirstyoudontsucceed
    Commented Aug 28, 2023 at 3:25
  • $\begingroup$ @ifatfirstyoudontsucceed Thanks a lot! $\endgroup$
    – Zhibin
    Commented Aug 28, 2023 at 3:43
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    $\begingroup$ Moreover, Djakov–Mitiagin (1976) construct a nuclear Fréchet space X such that for any nuclear Fréchet space Y the space X⨯Y has no basis. $\endgroup$
    – Dmitri Pavlov
    Commented Aug 28, 2023 at 18:16
  • $\begingroup$ @DmitriPavlov Thanks a lot! $\endgroup$
    – Zhibin
    Commented Aug 30, 2023 at 2:35

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