Difference between revisions of "Talk:Function vanishing at infinity"
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"In many cases $C_0(X)$ determines $X$, see e.g. Banach–Stone theorem" — Yes, but in Banach-Stone theorem $C_0(X)$ is treated as a Banach space (rather than Banach algebra; in the latter case the claim is almost trivial). [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:37, 10 January 2018 (CET) | "In many cases $C_0(X)$ determines $X$, see e.g. Banach–Stone theorem" — Yes, but in Banach-Stone theorem $C_0(X)$ is treated as a Banach space (rather than Banach algebra; in the latter case the claim is almost trivial). [[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 22:37, 10 January 2018 (CET) | ||
| + | :The concept of function vanishing at infinity is mentioned in the Banach–Stone theorem article but this does not seem particularly important point to make here. I suppose it's about reconstructing the space from the maximal ideals of the algebra, and then the functions that vanish at infinity form an ideal which does not correspond to a point of the space. [[User:Richard Pinch|Richard Pinch]] ([[User talk:Richard Pinch|talk]]) 08:38, 11 January 2018 (CET) | ||
Revision as of 07:38, 11 January 2018
"In many cases $C_0(X)$ determines $X$, see e.g. Banach–Stone theorem" — Yes, but in Banach-Stone theorem $C_0(X)$ is treated as a Banach space (rather than Banach algebra; in the latter case the claim is almost trivial). Boris Tsirelson (talk) 22:37, 10 January 2018 (CET)
- The concept of function vanishing at infinity is mentioned in the Banach–Stone theorem article but this does not seem particularly important point to make here. I suppose it's about reconstructing the space from the maximal ideals of the algebra, and then the functions that vanish at infinity form an ideal which does not correspond to a point of the space. Richard Pinch (talk) 08:38, 11 January 2018 (CET)
How to Cite This Entry:
Function vanishing at infinity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Function_vanishing_at_infinity&oldid=42711
Function vanishing at infinity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Function_vanishing_at_infinity&oldid=42711