All Questions
10 questions
0
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Is the space $C_0^{k}(\Omega)$ a Montel space?
I asked this question in the MathStackExchange, but I think I'm not get any answer.
I'm trying to find a reference for the following result:
Theorem: Let $\Omega$ be a open subset of $\mathbb{R}^{d}$ ...
- 509
0
votes
0
answers
192
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Reference request: an introduction to nuclear spaces
I am looking for a short introduction to nuclear spaces and nuclear operators. I am interested in these spaces as they often arise in mathematically rigorous quantum field theories. I have read the ...
- 721
3
votes
1
answer
210
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Reference on inductive (direct) limit of ordered vector spaces and vector lattices
I looked in all textbooks on vector lattices (Riesz spaces) as well as ordered vector spaces, but couldn't find any mentions of neither inductive nor projective limit for these structures. Googling ...
- 5,529
2
votes
3
answers
230
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Every linear topological space embeds into the Tychonoff product of linear metric spaces
I need a reference to the following (known?)
Fact. Every topological vector space $X$ over the field of real numbers is topologically isomorphic to a linear subspace of the Tychonoff product of ...
- 41.8k
2
votes
1
answer
236
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Closure in the strong dual topology
Originally asked on MSE.
Let $E$ be a metrizable locally convex topological vector space and let $E^{*}$ be its dual space endowed with the strong topology = topology of uniform convergence on (...
- 5,529
6
votes
0
answers
272
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Extension operators for topological vector space-valued smooth functions on closed sets
There are many known results about extension theorems for real-valued functions on closed sets, with varying levels of differentiability and so on, all very roughly following the Whitney approach. For ...
- 35.5k
2
votes
0
answers
459
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Weak topology on subsets of a normed space
I have few questions about the subsets of a normed space $X$ endowed with the weak topology. Let $E$ be such subset.
When is the norm a continuous function on $E$?
When is the metric induced by the ...
- 5,529
6
votes
4
answers
1k
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Reference for integral of functions taking values in a topological vector space.
(Note that I am interested in the Gelfand-Pettis integral specifically, as opposed to, for example, the Bochner integral.) I have tried Googling things like "integral topological vector space", "...
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8
votes
5
answers
545
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Reference for : a Fréchet nuclear space is Montel
I'm looking for a reference to cite regarding the property presented in the title: "Closed and bounded sets of a nuclear Fréchet space are compact"
Thank you in advance for the help!
- 5,428
5
votes
1
answer
510
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The space $H(D)$ of holomorphic functions.
A very natural example of a nuclear Montel space is the space $H(D)$ of all holomorphic functions on the open disc topologized by the family of seminorms
$$p_n(f)=\sup\{|f(z)|\colon |z|\leq 1-\tfrac{...
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