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Feb
4 |
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Riesz representation for an infinite-dimensional space
I looked up projective limit, but I don't see why $C(X)$ is the projective limit of $C(K)$. Would you please indicate what are the coordinate spaces and the bonding maps in the inverse limit? |
Feb
4 |
awarded | Commentator |
Feb
4 |
comment |
Riesz representation for an infinite-dimensional space
According to my topology book, there is a restriction. The statement, "a function on X is continuous iff its restrictions on compact subsets are continuous" requires X to be compactly generated. However, in my case X is compactly generated. |
Feb
4 |
comment |
Riesz representation for an infinite-dimensional space
@Yemon, which smaller space do you suggest to consider instead of $C(X)$? Do you know of a reference for Riesz representation for $C(X)$ where $X$ is a metrizable non LCH space? |
Feb
4 |
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Riesz representation for an infinite-dimensional space
What does it mean that $C(X)$ is the projective limit of $C(K)$? Does this require X to be a countable union of compact sets? |
Feb
4 |
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Riesz representation for an infinite-dimensional space
@Yemon, You are misunderstanding the question. I give you a Banach algebra $X$ that is infinite dimensional. I am asking for a topology on $C(X)$ and a characterization of its dual. I am asking if anyone has seen such sort of theorem. The focus is the infinite-dimensionality of $X$. Either you have seen a Riesz-type theorem for infinite-dimensional spaces or not. If you don't like $X$ being an algebra, assume it's just a Banach space, or assume it's just a topological vector space. |
Feb
3 |
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Riesz representation for an infinite-dimensional space
$C(X)$ can be given a topology (most likely not a normable), but I don't want to specify one because that is part of the question. I am asking if there is some sort of Riesz representation theorem for an infinite-dimensional space $X$ where $C(X)$ has some nontrivial topology? |
Feb
3 |
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Riesz representation for an infinite-dimensional space
Is $C(X)$ suppose to be a Banach space? |
Feb
3 |
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Riesz representation for an infinite-dimensional space
I didn't say $C(X)$ is a Banach space. |
Feb
3 |
asked | Riesz representation for an infinite-dimensional space |
Dec
4 |
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Absolutely Continuous Invariant Measures for Piecewise Convex Maps
You can get away with $C^{1+\alpha}$, but with less regularity, I'm not sure. |
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3 |
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3 |
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Absolutely Continuous Invariant Measures for Piecewise Convex Maps
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Dec
3 |
answered | Absolutely Continuous Invariant Measures for Piecewise Convex Maps |
Oct
26 |
answered | Applications of Hilbert's metric |
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19 |
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17 |
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15 |
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14 |
answered | Fundamental Examples |
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22 |
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