Timeline for Does weak $L^2$ approximation implies $L^2$ approximation under a condition similar to convexity?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 25, 2023 at 3:47 | comment | added | David Gao | @NarutakaOZAWA Ah, so the set of all self-adjoint unitaries would be a counterexample. Thank you so much! | |
| Dec 25, 2023 at 2:28 | comment | added | Narutaka OZAWA | The same holds for the real case. For example, iid Rademacher variables are orthonormal and hence contain zero in the weak $L^2$ closure. | |
| Dec 22, 2023 at 8:51 | history | edited | David Gao | CC BY-SA 4.0 |
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| Dec 22, 2023 at 8:44 | comment | added | David Gao | @NarutakaOZAWA You’re right. Guess this isn’t true in general. Do you think a similar counterexample could exist if we also assume all functions in $S$ are real-valued? The unitary example doesn’t seem easily adaptable to that. | |
| Dec 22, 2023 at 8:32 | comment | added | Narutaka OZAWA | The set $S$ of unitary functions contains zero in the weak $L^2$ closure. | |
| Dec 22, 2023 at 3:20 | history | asked | David Gao | CC BY-SA 4.0 |