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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

6 votes
2 answers
353 views

Complete dual of bornological space

A bornologigal topological vector space is such that any bounded linear function on it is continuous. It is a standard result [Jarchow, Locally convex spaces, 1981] that if the dual $E'$ of a Mackey s …
James's user avatar
  • 103
4 votes
1 answer
175 views

DF-spaces and F spaces

It is well known that when $E$ is a $DF$-space and $F$ is a Fréchet space, the space $\mathcal{L}_{b} (E,F)$ is Fréchet. The converse, that is the fact that $\mathcal{L}_{b} (F,E)$ would be $DF$, is i …
James's user avatar
  • 103