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2d

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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Actually, I don't understand... For which Stein manifold $N$ we have ${\mathcal O}(N)={\mathbb C}[\varepsilon]/\varepsilon^2$? 
2d

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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
@nfdc23, is it possible that this is simpler? Let $I_s$ be the ideal of functions in ${\mathcal O}(M)$ vanishing at the point $s\in M$. Actually, I need the following: if a system of functions $f_1,...,f_n\in {\mathcal O}(M)$ form local coordinates in a point $s\in M$ and $f_1(s)=...=f_n(s)=0$, then for any $f\in {\mathcal O}(M)$ the function $ff(s)\lambda_1 f_1...\lambda_n f_n$ belongs to $(I_s)^2$, where $\lambda_i$ are the partial derivatives of $f$ in the point $s$ along the coordinates $f_i$. Is this true? 
May
1 
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
OK, thank you!! 
May
1 
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Ben, I can't get this paper. Does Rossi prove the homeomorphism of topological spaces or just the equality of sets? 
May
1 
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Ah, OK! And what about the tangent space? 
Apr
29 
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Why do we study symplectic geometry?
Questions about applications are very important, and, by the way, they inspire research. It is not good to close them. 
Apr
24 
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Attempted Banachification of a space
Will, I am a bit far from this now, this is just my feeling. Can you reformulate your definition in categorical terms (i.e. using linear continuous maps as arrows)? 
Apr
24 
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Attempted Banachification of a space
This reminds of the bornologification: books.google.ru/…, or arxiv.org/abs/1110.2013, page 44, example 1.13. I believe, the differences, if any, are not essential. 
Apr
7 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@Yemon, independently on how we define the borders, the questions about applications  "why are you doing (/interested in) this?"  are inevitable. Is there a possibility to ask this at MO (or anywhere else)? And do you agree that people who ask this have right to do this? 
Apr
6 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@Yemon, in my opinion your doubts about Beurling and the rest are not very serious. There must be more clear rules for decisions like this. 
Apr
6 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@IanMorris, I understand you, but there is a difference between some random titles of the articles in GAFA and a possibility to speak with people who have their own opinion on this question. 
Apr
6 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@IanMorris, some people don't have access to mathscinet. 
Apr
5 
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Which complete Boolean algebras arise as the algebras of projections of commutative von Neumann algebras?
Yes, I meant this. OK. 
Apr
5 
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Which complete Boolean algebras arise as the algebras of projections of commutative von Neumann algebras?
@DmitriPavlov, are there any generalizations of these constructions to noncommutative case? 
Mar
28 
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A linear functional on $C(K)^*$ continuous on each $L_1(\mu)$
Of course! Actually, I think there must be a reminder for people like me, who don't know things like this. Say, a button "cross post" with an explanation when it should be used. 
Mar
28 
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A linear functional on $C(K)^*$ continuous on each $L_1(\mu)$
Nate, excuse me, I did not know about this rule. I already apologized to David Ullrich. 
Mar
25 
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Sequentiality of largest vector topology
Ah, OK, I am sorry. 
Mar
24 
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Sequentiality of largest vector topology
It seems to me I saw something similar here: link.springer.com/article/10.1007%2FBF01234921 Perhaps, this will help. 
Mar
23 
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Sequentiality of largest vector topology
What do you mean by "vector topology"? 
Mar
6 
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Is the Mendeleev table explained in quantum mechanics?
Anyway, the words "Postulates of quantum mechanics", en.wikipedia.org/wiki/…, must mean something. If they are not the same as postulates (or axioms) in Mathematics, then there must be an explanation of their meaning. Otherwise this becomes an abuse of the trust of a listener, isn't it? 