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1 vote
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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 $K$ ...
Ayman Moussa's user avatar
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2 votes
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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 ...
David White's user avatar
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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&...
TaQ's user avatar
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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 ...
rediscoveringamerica's user avatar
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} \...
Iosif Pinelis's user avatar

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