Timeline for Smooth function algebra on cartesian product and beyond
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 24, 2022 at 13:34 | comment | added | Jochen Wengenroth | 9 years ago I probably meant by $\otimes_i$ the inductive tensor product of Grothendieck which differs for the injective tensor product $\otimes_\varepsilon$. | |
| Apr 23, 2022 at 20:58 | comment | added | Z. M | @JochenWengenroth Sorry for my confusion about your notations. What is $\otimes_i$? I guess that $\otimes_\epsilon$ is with $\epsilon$-topology, and $\otimes_\pi$ is with $\pi$-topology (in Treves' terms)? | |
| Nov 12, 2020 at 18:28 | comment | added | user126256 | I know this question is super old, but: Jochen's comment and Peter's answer seem to contradict each other, no? Jochen says that the projective tensor product of compactly supported functions on $\mathbb{R}$ does not equal the compactly supported functions on the product space, but the last sentence in Peter's answer appears to say that it does. The cited Treves page seems not to comment on this situation (he only considers the product of the compactly supported function on compact spaces). If one of you sees this, could you clarify? | |
| Mar 21, 2013 at 12:18 | comment | added | Jochen Wengenroth | Just a little remark: That $\otimes_i$ coincides with $\otimes_pi$ in this case is not only because of nuclearity (your remark about the spaces of smooth functions with compact support shows this since $\mathscr D(\mathbb R) \tilde{\otimes}_\pi \mathscr D(\mathbb R) \neq \mathscr D(\mathbb R^2)$).You use first that $\otimes_i = \otimes_\varepsilon$ for Frechet spaces and then nuclearity. | |
| Mar 19, 2013 at 19:35 | history | edited | Peter Michor | CC BY-SA 3.0 |
added 80 characters in body
|
| Mar 19, 2013 at 19:27 | vote | accept | Nevermind | ||
| Mar 19, 2013 at 19:11 | history | edited | Peter Michor | CC BY-SA 3.0 |
added 52 characters in body
|
| Mar 19, 2013 at 18:37 | history | answered | Peter Michor | CC BY-SA 3.0 |