Timeline for Dominated convergence theorem for Banach limits
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2022 at 0:28 | comment | added | Arbiter | Of course it wont hold for everything. We should ask for some form of uniform bound $g_n$ (independent of $t$ and summable) on the $|f_n(t)|$, like in the assumption of the dominated convergence theorem. That is my question, do we have an analogue of the dominated convergence theorem here? | |
| Mar 29, 2022 at 21:39 | comment | added | Michael Greinecker | Doesn't that already fail for the usual Banach limit on $\ell_\infty$? Let $\mathbf{1}$ be the constant sequence with value $1$ and let $\mathbf{1}_n$ be the sequence with a $1$ in the $n$th place and all other entries $0$. Then $\mathbf{1}=\sum_{n=1}^\infty \mathbf{1}_n$. But $L(\mathbf{1})=1\neq 0=\sum_{n=1}^\infty L(\mathbf{1}_n)$. The point is that Banach limits coincide with the usual limits when they exist. | |
| Mar 29, 2022 at 21:14 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Mar 29, 2022 at 19:31 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing
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| S Mar 29, 2022 at 19:22 | review | First questions | |||
| Mar 29, 2022 at 19:39 | |||||
| S Mar 29, 2022 at 19:22 | history | asked | Arbiter | CC BY-SA 4.0 |