Timeline for Example of a ‘weak’ ideal which is not an ideal?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2021 at 18:56 | comment | added | Matthew Daws | I think you should ask a new question, being very precise about what your question is. | |
| Mar 3, 2021 at 17:51 | comment | added | Arpit Kansal | @MatthewDaws: Unfortunately the OP hasn’t replied but assuming the ‘usual’ understanding of product do you think both concepts coincide? Even after trying hard, I could get a counterexample. | |
| Mar 3, 2021 at 12:26 | comment | added | Matthew Daws | @ArpitKansal I was trying to understand what the OP meant by what they wrote... | |
| Mar 3, 2021 at 9:15 | comment | added | Arpit Kansal | @MatthewDaws: Sorry, by taking product of definition as yours did you mean span$(IV^*V-VV*I)=IV^*V-VV^*I$? I don’t see it. Am I missing something obvious? | |
| Feb 24, 2021 at 17:10 | comment | added | Matthew Daws | Actually, I don't understand the notation, because when you write something like "$V^*V$" I take this to be defined to be a linear span, namely $\operatorname{span}\{ x^*y : x,y\in V \}$. So I don't understand the difference in definition between "ideal" and "weak ideal". | |
| Feb 24, 2021 at 14:22 | comment | added | Math Lover | @MatthewDaws: In general, the same could be defined for any TRO $V$ but I was wondering if there is some example for the TRO B(H,K). Do you have example of weak ideal for some TRO $V$ other than $B(H,K)$? | |
| Feb 24, 2021 at 9:26 | comment | added | Matthew Daws | Even with the edit, $V$ is still defined to be the whole of $B(H,K)$. This is surely too strong a condition. Do you perhaps want $V$ to be a TRO? | |
| Feb 24, 2021 at 3:56 | history | edited | Math Lover | CC BY-SA 4.0 |
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| Feb 24, 2021 at 3:54 | comment | added | Math Lover | @MatthewDaws: Sorry you’re right, I means to be sub space of B(H,K). | |
| Feb 24, 2021 at 3:53 | comment | added | Math Lover | @YemonChoi: I don’t have references for the ‘weak’ ideal definition, it’s something i am trying to define. As far as ideal is concerned, it’s usually known as TRO ideal. | |
| Feb 24, 2021 at 3:48 | history | edited | Math Lover | CC BY-SA 4.0 |
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| Feb 23, 2021 at 19:59 | comment | added | Yemon Choi | @MatthewDaws I think this must all be TRO related, and I suspect the OP has taken definitions pertaining to general TROs and tried to specialize to particular cases. To the OP: perhaps you could give references for the definitions you are presenting here? | |
| Feb 23, 2021 at 19:23 | comment | added | Matthew Daws | So $H,K$ are Hilbert spaces? I think you must have made a mistake: if $H,K$ are both separable infinite dimensional (for example) and $V = B(H,K)$ then $V^*V = B(H)$ and $VV^* = B(K)$. Is $I$ means to be a subspace of $B(H,K)$? | |
| Feb 23, 2021 at 16:48 | history | asked | Math Lover | CC BY-SA 4.0 |