Timeline for Does there exists a $C^*$-algebra corresponding to every Banach ternary algebra?
Current License: CC BY-SA 4.0
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| Jun 22, 2021 at 7:46 | answer | added | Matthew Daws | timeline score: 3 | |
| Jun 20, 2021 at 16:06 | history | edited | Math Lover | CC BY-SA 4.0 |
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| Jun 20, 2021 at 15:59 | comment | added | Math Lover | @YemonChoi: I was thinking in the setting of general ternary Banach algebras. After some googling I found out this paper which discusses what I am looking for but unfortunately I don't get any intuition for the construction given in the paper. | |
| Jun 20, 2021 at 14:12 | comment | added | Yemon Choi | Indeed, given your opening paragraph, which discusses how a TRO can be analyzed in terms of an associated Cstar algebra, surely the most natural parallel for ternary Banach algebras is to try and analyse a "TBA" in terms of some associated Banach algebra? | |
| Jun 20, 2021 at 14:10 | comment | added | Yemon Choi | How general do you want your ternary Banach algebras to be? There exist (commutative!) Banach algebras A such that the only homomorphism from A to B(H) is the zero map, so that even if one tries to construct some kind of functorial "enveloping Cstar algebra" for Banach algebras, the resulting object might not detect any of the original structure of A. I imagine that things will only be worse in the setting of general ternary Banach algebras | |
| Jun 20, 2021 at 12:53 | history | edited | YCor | CC BY-SA 4.0 |
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| Jun 20, 2021 at 10:25 | history | asked | Math Lover | CC BY-SA 4.0 |