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May 20, 2022 at 3:52 vote accept Math Lover
May 19, 2022 at 7:35 vote accept Math Lover
May 20, 2022 at 3:51
Oct 30, 2021 at 21:39 comment added Ruy @MathLover, I don't think there is a meaningful linking C*-algebra for an anti-TRO $X$. If there was one, then that algebra would embedd into $B(H)$, and hence so would $X$, but we know $X$ cannot be represented in $B(H)$ (unless you are willing to disregard its ternary product).
Oct 30, 2021 at 1:19 comment added Math Lover @Ruy: Thank you very much for an informative answer. Do you any notion of “linking $C^*$-algebra” for Ternary $C^*$-rings like we have for TROs? Zettl’s $C^*$-algebra does not quite qualify to be “linking $C^*$-algebra” as two non isomorphic ternary $C^*$-rings also can have isomorphic $C^*$-algebras.
Oct 29, 2021 at 23:34 history edited Ruy CC BY-SA 4.0
added 2 characters in body
Oct 29, 2021 at 23:31 comment added Ruy @LSpice, the last paragraph in my latest edit might help one to see what is wrong with anti-TRO's.
Oct 29, 2021 at 23:29 history edited Ruy CC BY-SA 4.0
Added last paragraph
Oct 29, 2021 at 17:00 comment added LSpice Thanks! This definitely makes clear that you might obtain a new algebra from the old one in a particularly simple fashion. But is it clear that this new, different algebra does not embed in some new, different operator algebra? I think I must be misreading your description, because it seems to me that you are saying that every ternary $C^*$-ring does embed in an operator algebra in a particularly rigid way.
Oct 29, 2021 at 14:31 comment added Ruy @LSpice, I've edited my answer hopping to clarify my point. Indeed my original answer was a bit terse!
Oct 29, 2021 at 14:27 history edited Ruy CC BY-SA 4.0
Complete rewriting
Oct 29, 2021 at 11:51 comment added LSpice @WlodAA, thanks! I have deleted my wrong comments about parity.
Oct 29, 2021 at 2:27 history edited LSpice CC BY-SA 4.0
Typo
Oct 29, 2021 at 2:26 comment added LSpice Is it clear that this does not embed in some (possibly different) operator algebra? Maybe this is what you mean by decomposing uniquely into a positive part and a negative part, but I don't know what that means.
Oct 28, 2021 at 23:31 history edited Ruy CC BY-SA 4.0
added 258 characters in body
Oct 28, 2021 at 23:26 history answered Ruy CC BY-SA 4.0