All Questions
10 questions
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
6
votes
4
answers
1k
views
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", "...
- 1,270
6
votes
0
answers
272
views
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
5
votes
1
answer
510
views
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{...
- 51
3
votes
1
answer
210
views
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
views
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
views
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
2
votes
0
answers
459
views
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
0
votes
1
answer
143
views
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
views
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 ...
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