Timeline for Special bound of net and inequality
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2016 at 11:26 | vote | accept | Hamid Shafie Asl | ||
| Dec 14, 2016 at 15:11 | comment | added | Jochen Wengenroth | @YemonChoi But nevertheless, a convergent net needn't be bounded. | |
| Dec 12, 2016 at 16:44 | answer | added | Yemon Choi | timeline score: 1 | |
| Dec 12, 2016 at 16:07 | comment | added | Yemon Choi | Your latest version is phrased in a strange way. If you think about your last sentence, you seem to be asking "is $K \geq \Vert m\Vert$? | |
| Dec 12, 2016 at 16:03 | comment | added | Yemon Choi | @NateEldredge Oops, yes you are right :) I tend to use the result with $x_i \to x$ weakly, but since the OP has already used the Mazur trick to improve weak convergence to norm convergence, then there is no need for Hahn-Banach | |
| Dec 12, 2016 at 16:00 | comment | added | Nate Eldredge | @YemonChoi: Isn't it really just the triangle inequality? | |
| Dec 12, 2016 at 15:43 | history | edited | Yemon Choi |
The question has nothing to do with AHA or OA
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| Dec 12, 2016 at 15:43 | comment | added | Yemon Choi | By the way, if a net $(x_i)$ in a Banach space $E$ converges in the norm topology to some $x\in E$, then we always have $\Vert x \Vert \leq \sup_i \Vert x_i\Vert$. This follows from the Hahn-Banach theorem, and is "core functional analysis" that has nothing to do with Banach algebras, or amenability. | |
| Dec 12, 2016 at 15:16 | history | edited | Hamid Shafie Asl | CC BY-SA 3.0 |
added 48 characters in body
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| Dec 12, 2016 at 9:27 | comment | added | Pietro Majer | I'm a bit confused about the role of the net in the last assumption. From one side, this net may be, in particular, the constant net (which we can't exclude without further information). On the other side, if that assumption is verified by some $\{m_\alpha\}$, then by continuity of $\Delta$ it is also true for the constant net $m_\alpha=m$, with the same $K$. So why this assumption should be any stronger that just asking $\|a\Delta(m)\|\le K\|a\|$? | |
| Dec 12, 2016 at 5:10 | comment | added | Hamid Shafie Asl | Dear @Pietro Majer, I edited my question | |
| Dec 12, 2016 at 5:09 | history | edited | Hamid Shafie Asl | CC BY-SA 3.0 |
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| Dec 11, 2016 at 16:04 | history | asked | Hamid Shafie Asl | CC BY-SA 3.0 |