New answers tagged topological-vector-spaces
1
vote
Accepted
Is the space $C_0^{k}(\Omega)$ a Montel space?
In the following I write $C^k_K(\Omega)$ for the space of all $C^k(\Omega)$ functions having support included in $K$, equipped with its "natural" norm $\|\cdot\|_{K,k}$ (uniform norm on $K$ ...
2
votes
Accepted
Factorization systems for vector bundles
Normally, we consider vector bundles over some base space $X$. The simplest case is if $X$ is a point. Then the category of vector bundles over $X$ is just the category of vector spaces (over whatever ...
3
votes
Does the uniform boundedness principle holds for multilinear maps as well?
First, I think this is the type of questions that MO is for.
Second, Iosif Pinelis has already given an accepted answer, but for the record I give the following. "Uniform boundedness principle&...
4
votes
Does the uniform boundedness principle holds for multilinear maps as well?
It follows easily from the standard case (for linear mappings) that the pointwise limit is separately continuous and a standard result states that separately continuous multi-linear mappings (say on ...
8
votes
Accepted
Does the uniform boundedness principle holds for multilinear maps as well?
$\newcommand{\om}{\omega}$Let me answer your specific question.
The proof is similar to that of the uniform boundedness principle for linear functionals, but here using the identity
\begin{equation}
\...
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