Timeline for Fredholm $C^*$-algebras
Current License: CC BY-SA 4.0
31 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2021 at 8:57 | vote | accept | Ali Taghavi | ||
| Oct 21, 2021 at 16:12 | answer | added | Alain Valette | timeline score: 1 | |
| S Oct 18, 2021 at 0:04 | history | bounty ended | CommunityBot | ||
| S Oct 18, 2021 at 0:04 | history | notice removed | CommunityBot | ||
| S Oct 9, 2021 at 21:53 | history | bounty started | Ali Taghavi | ||
| S Oct 9, 2021 at 21:53 | history | notice added | Ali Taghavi | Draw attention | |
| S Dec 20, 2020 at 14:00 | history | bounty ended | CommunityBot | ||
| S Dec 20, 2020 at 14:00 | history | notice removed | CommunityBot | ||
| Dec 12, 2020 at 19:41 | comment | added | Ali Taghavi | @YCor Any way one can consider both properties with two different name. But it seems that the irreducible one is more interesting(and less obvious). | |
| Dec 12, 2020 at 19:09 | comment | added | Ali Taghavi | @YCor However I am not sure I am convinced by answer of Nik Weaver. I should rea his answer again. | |
| Dec 12, 2020 at 18:58 | comment | added | Ali Taghavi | @YCor Thanks for your recent edit of my question. But there is a question in my mind since many years ago. Some times a user edit my post. When I look at his edit I realize that some words is edited without any change. for example in the second paragraph you changed "algebras"to again "algebras". What is the reason for this situation? | |
| Dec 12, 2020 at 18:53 | comment | added | Ali Taghavi | @YCor The first one. Please see the answer by Nik Weaver. | |
| Dec 12, 2020 at 18:45 | comment | added | Ali Taghavi | @YCor apart from these cases. it would be interesting to find some non examples. | |
| Dec 12, 2020 at 18:43 | comment | added | YCor | But your questions give two definitions of Fredholm C$*$-algebra. Which one of the two questions is supposed to characterize them? | |
| Dec 12, 2020 at 18:42 | comment | added | Ali Taghavi | @YCor Yes I see. Any way as you said every algebra with finite dimensional quotien is a fredholm algebra. | |
| Dec 12, 2020 at 18:36 | comment | added | YCor | No, irreducible is clearly defined (=nonzero and no proper nonzero closed invariant subspace). "Trivial" is slightly more ambiguous since it can be the trivial irrep (1-dimensional), or any trivial representation (which can be in dimension 0, 1, or more). | |
| Dec 12, 2020 at 18:30 | comment | added | YCor | Actually I especially amended my comment. So, for the first question, this class contains all C$*$-algebras that admit a nonzero finite-dimensional representation, i.e., admit a nonzero finite-dimensional quotient. | |
| Dec 12, 2020 at 17:58 | comment | added | Ali Taghavi | @YCor I do not know. by definition, if we consider the zero representation on $H=\mathbb{C}$ as an irreducible representation. any way why should be worry about it? what do you mean by "but actually this trivial 1 dimensional representation does not exist". I think the question is clear, do you agree? | |
| Dec 12, 2020 at 16:14 | comment | added | YCor | Oh, but actually this trivial 1-dimensional rep doesn't always exist... maybe my comment was stupid. I see no reason in particular to single out the trivial 1-dimensional rep among all finite-dimensional irreducible reps. | |
| Dec 12, 2020 at 16:05 | comment | added | Ali Taghavi | @YCor Good point! one may add "non trivial representation" | |
| Dec 12, 2020 at 14:34 | comment | added | YCor | How do you exclude the trivial 1-dim rep for the first question? | |
| Dec 12, 2020 at 14:34 | history | edited | YCor | CC BY-SA 4.0 |
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| S Dec 12, 2020 at 12:46 | history | bounty started | Ali Taghavi | ||
| S Dec 12, 2020 at 12:46 | history | notice added | Ali Taghavi | Authoritative reference needed | |
| Sep 6, 2020 at 2:17 | answer | added | Nik Weaver | timeline score: 6 | |
| Sep 6, 2020 at 2:09 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Sep 6, 2020 at 1:21 | comment | added | Ali Taghavi | and P is an arbitrary polynomial of degree at most n | |
| Sep 6, 2020 at 1:16 | comment | added | Ali Taghavi | $\{P(s)\mid s\text{ is the shift operator, whose index is -1}\}$ | |
| Sep 6, 2020 at 1:12 | comment | added | Ali Taghavi | @YemonChoi Trivial examples: Finite dimensions. Or in the case of infinite dimension, the scalar 1 dimensional space. or any subspace which does not contain any fredholm operator. As another example the space of $\{P(s)\mid s\text{ is the shift operator, whose index is -1 and P is an arbitrary polynomial of degree at most n\}$ | |
| Sep 6, 2020 at 1:09 | comment | added | Yemon Choi | Do you have an example of a Fredholm subspace? | |
| Sep 6, 2020 at 0:42 | history | asked | Ali Taghavi | CC BY-SA 4.0 |