Timeline for $C[0,1]$ is Banach-space isomorphic to $c_0(C[0,1])$
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2016 at 4:29 | comment | added | Bill Johnson | In Banach space theory, isomorphism means linear homeomorphism. This is completely standard. | |
| Feb 25, 2016 at 23:58 | history | edited | Li Jingyang | CC BY-SA 3.0 |
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| Feb 25, 2016 at 17:22 | comment | added | Todd Trimble | @YemonChoi (Referring to your second comment) I defer to your judgment here, although I've seen "linearly homeomorphic" also used to indicate the weaker notion of isomorphism (and FWIW, I personally believe that would be preferable language). | |
| Feb 25, 2016 at 17:04 | comment | added | Yemon Choi | @ToddTrimble As I think was discussed on the nLab a while ago, "isometrically isomorphic" is not usually used as the default by people who work with Banach spaces - if we want isometric we usually feel obliged to explicitly mention it | |
| Feb 25, 2016 at 17:02 | comment | added | Yemon Choi | @ToddTrimble I think (but I don't claim to speak for everyone) that "Banach-space isomorphic" is in contrast to "Banach-algebraically isomorphic" (both objects are Cstar algebras, so if one just said "isomorphic", one might think this is isomorphism of Cstar algebras) | |
| Feb 25, 2016 at 16:05 | answer | added | Jochen Wengenroth | timeline score: 3 | |
| Feb 25, 2016 at 15:37 | comment | added | Todd Trimble | Is Banach-space isomorphic the term you want? Ordinarily I think of "Banach-space isomorphic" as synonymous with isometrically isomorphic. | |
| Feb 25, 2016 at 14:15 | vote | accept | Li Jingyang | ||
| Feb 25, 2016 at 13:21 | answer | added | Fedor Petrov | timeline score: 3 | |
| Feb 25, 2016 at 13:05 | history | edited | Fedor Petrov |
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| Feb 25, 2016 at 12:45 | review | First posts | |||
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| Feb 25, 2016 at 12:41 | history | asked | Li Jingyang | CC BY-SA 3.0 |