Timeline for Subtle distinction in "completeness"?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2022 at 15:39 | comment | added | Yemon Choi | @LSpice Banach algebraists often call this "unitization" (it does what it says on the tin) | |
| Sep 12, 2022 at 15:39 | comment | added | Yemon Choi | As @QiaochuYuan points out below, this is nothng to do with "completeness" in the sense of metric spaces. The Banach space $L^1({\bf R})$ is complete in its usual norm and is a Banach algebra when equipped with the convolution product. However it does not have an identity element for convolution (this would be the Dirac delta, as you observe) | |
| Aug 29, 2022 at 18:09 | history | edited | YCor |
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| Aug 29, 2022 at 1:52 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Aug 28, 2022 at 23:52 | comment | added | LSpice | This is an example (though I'd never thought of it as such, and it's more concrete than the usual abstract such process) of adjoining a unit to an algebra that doesn't have one, but I don't know any other name for that than "adjoining a unit". | |
| Aug 28, 2022 at 23:45 | history | edited | askquestions2 | CC BY-SA 4.0 |
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| Aug 28, 2022 at 23:34 | history | asked | askquestions2 | CC BY-SA 4.0 |