Timeline for Elementary + short + useful
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 29, 2011 at 2:10 | comment | added | Paul Siegel | @L Spice - Perhaps this one is a stretch, especially for a 30 minute talk. But I could imagine using this result as motivation for the abstract definition of a ring. One could start out by defining C_0(X) as just a set of functions and then start listing its extra structure. Then one can pose the question: how much structure do we need to pile on before we have enough information to recover X? I've never actually tried giving a talk like this, but it doesn't seem totally inconceivable. | |
| Apr 10, 2011 at 9:18 | comment | added | Yemon Choi | Personally, I view it as a theorem telling me that (locally) compact Hausdorff spaces can be wild and savage beasts. Though as Paul says, it is the result which allows one to construct continuous functional calculus for normal elements in C*-algebras, and that is most definitely a useful "tool-type" theorem | |
| Apr 8, 2011 at 19:12 | comment | added | Kevin Ventullo | +1. I don't study C*-algebras, but this is one of the prettiest theorems I know. This is definitely a "jewelry-type" theorem. On the other hand, the non-commutative analogue (GNS construction) lies at the foundation of the theory of operator algebras; I think most functional analysts would view this as a "tool-type" theorem. | |
| Apr 8, 2011 at 18:09 | comment | added | LSpice | I know that playing “elementarier-than-thou” isn't really much fun, but how can you possibly conceive of this as a lecture with no prerequisites? For example, it seems doubtful that one could convince students (usefully) that a ring is a geometric object if they didn't first have the idea that a ring was an algebraic object …. | |
| Apr 5, 2011 at 16:56 | history | answered | Paul Siegel | CC BY-SA 2.5 |