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While reading about quojections and prequojections in the book "Advances in the Theory of Fréchet Spaces," I'm having trouble understanding why every quojection is necessarily a prequojection. Could someone clarify the reasoning behind this?
by the way A quojection is a Fréchet space that can be represented as a projective limit of Banach spaces connected by surjective maps. A prequojection is a Fréchet space whose bidual (the dual of its dual space) is a quojection.

Assalami Med
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    It would be very useful, to make this post more helpful to general readers and easier for others to answer, if you would define "quojection" and "prequojection" – FShrike Jun 15 '24 at 18:59
  • A quojection is a Frechet space that can be represented as a projective limit of Banach spaces connected by surjective maps. A prequojection is a Frechet space whose bidual (the dual of its dual space) is a quojection. – Assalami Med Jun 16 '24 at 10:15
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    Right. Well then the reasonable guess is that application of the bidual functor to the limit describing a given quojection $V$ would yield a limit diagram for $V^{\ast\ast}$. I'm not sure of the details though, we would need to assume $(-)^{\ast\ast}$ is a continuous functor on the category of Banach spaces – FShrike Jun 16 '24 at 12:27
  • I would appreciate more details if you could – Assalami Med Jun 16 '24 at 12:31
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    I’m not sure of them! I’ll wait for someone with more confidence in this kind of functional analysis to answer – FShrike Jun 16 '24 at 12:33
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    I appreciate your help anyway – Assalami Med Jun 16 '24 at 12:41

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