Timeline for A characterisation of certain $C^*$-algebras
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 31, 2018 at 11:29 | comment | added | Caleb Eckhardt | @MarkRoelands Yes that is what I mean to say (unless you by 'atom' you mean something different than 'minimal projection'). Non-zero positive functionals won't give you a one-dimensional C*-algebra quotient unless those functionals happen to be multiplicative. | |
| Oct 31, 2018 at 8:49 | comment | added | Mark Roelands | @ Caleb Eckhardt. Do you mean to say that $A$ has no ideals of co-dimension one if and only if $A^{**}$ has no central atoms, because non-zero functionals always give you one-dimensional quotients? | |
| Oct 29, 2018 at 16:19 | comment | added | Caleb Eckhardt | I'm not sure what kind of condition you are looking for. But if you just translate '$A^{* *}$ has a projection that is both central and minimal' into a statement about $A$ you obtain '$A$ has a one-dimensional quotient.' | |
| Oct 28, 2018 at 10:30 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
added 27 characters in body; edited title
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| Oct 28, 2018 at 6:50 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
corrected a minor typo + added a Google Books link
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| S Oct 27, 2018 at 11:51 | history | suggested | Ali Taghavi |
I add a tag.
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| Oct 27, 2018 at 11:36 | review | Suggested edits | |||
| S Oct 27, 2018 at 11:51 | |||||
| Oct 27, 2018 at 9:43 | comment | added | Mark Roelands | You could ask the same question for JB-algebras: Is there a characterisation for those JB-algebras that have no central projections in the bidual? | |
| Oct 27, 2018 at 9:37 | comment | added | YCor | OK thanks, but how is this connected to the question? | |
| Oct 27, 2018 at 9:00 | comment | added | Mark Roelands | Because the self-adjoint part of a $C$*-algebra is a Jordan algebra (in fact it is a JB-algebra) with the product $x\circ y:=\frac{1}{2}(xy+yx)$. | |
| Oct 27, 2018 at 8:44 | comment | added | YCor | Why the tag jordan-algebra (a Jordan-algebra is a [non-necessarily-associative] commutative algebra satisfying the axiom $(xy)(xx)=x(y(xx))$)? | |
| Oct 27, 2018 at 8:20 | history | asked | Mark Roelands | CC BY-SA 4.0 |