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Aug 25, 2021 at 1:09 comment added Narutaka OZAWA The latter formula holds true for an arbitrary left TRO ideal. I just wanted to show how to find the right formula.
Aug 25, 2021 at 0:35 comment added Math Lover So we don't get the bijection between arbitrary left(right) ideals?
Aug 25, 2021 at 0:21 comment added Narutaka OZAWA Thank you. I miscalculated. In the easy case where $I=Vp$ for some projection $p\in [V^*V]$, the left ideal $L$ should be $A(1\oplus p)$ i.e., $L:=\left[\begin{matrix} [VV^*] & I \\ V^* & [V^*I]\end{matrix}\right]$.
Aug 24, 2021 at 15:57 comment added Math Lover It seems we need to use $ V^*VI^* \subset I^*$ for a left TRO ideal $I$. Is it obvious?
Aug 9, 2021 at 5:50 vote accept Math Lover
Aug 6, 2021 at 7:08 history edited Narutaka OZAWA CC BY-SA 4.0
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Aug 6, 2021 at 4:05 history answered Narutaka OZAWA CC BY-SA 4.0