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Results tagged with topological-vector-spaces
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user 12482
A topological vector space is a vector space $V$ over a topological field $\mathbb{K}$ (typically $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$), together with a topology on $V$ such that vector addition and scalar multiplication are both continuous. Hilbert spaces and Banach spaces are examples of topological vector spaces.
6
votes
How general is the convergence of the exponential function's power series?
Let me give you a counter-example with an associative $\beta$, i.e. a Frechet algebra for which the exponentials do not exist in general: The main reason is that a Frechet algebra needs not to be loca …
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2
votes
Reference for : a Fréchet nuclear space is Montel
Maybe not in a single theorem, but you can go for Cor1 in Section 33 and Cor3 in Section 50 in Treves book.
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1
vote
General theory for p-normed spaces
This is probably not quite an answer to your question but rather a hint how a generalization should look like. As already mentioned in the comments, the discrete and continuous measure-theoretic $\ell …
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3
votes
On Köthe sequence spaces
OK, on request, the following reference as answer:
Pietsch, A.: Nuclear locally convex spaces, vol. 66 in Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, New York, Heidelberg, 1972 …
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