Timeline for "Category" of Nonempty Metric Spaces and Contractive Maps?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 21, 2012 at 9:15 | comment | added | Chris Heunen | Such notions of ideals have been worked out in arxiv.org/abs/math/9805102, for example. They cover Hilbert-Schmidt maps, such as in Andrew's answer, and trace class operators, as in Kevin's comment. One would think the ideal of contractions could be axiomatized similarly. | |
| Feb 18, 2010 at 14:36 | comment | added | Kevin Buzzard | It's fun to occasionally see a fairly "natural" definition which is not satisfied by the identity map. The notions of trace class or compact maps on Hilbert spaces is another example: the identity map on a Hilbert space is trace class iff the space is finite-dimensional. In this case I always felt that what was going on was that the functions you're interested in are somehow an "ideal" in the space of all functions. For example if f is trace class and g is continuous then f o g is trace class. Similarly if f is a contraction map and g is non-expansive then f o g is a contraction. | |
| Feb 18, 2010 at 13:40 | vote | accept | Neel Krishnaswami | ||
| Feb 18, 2010 at 11:51 | answer | added | Andrew Stacey | timeline score: 3 | |
| Feb 18, 2010 at 11:39 | history | asked | Neel Krishnaswami | CC BY-SA 2.5 |