Timeline for Representations of Banach algebras
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2020 at 16:33 | comment | added | Paul Visoianu | T_L (A) is not in general a C*-algebra even if A is. Am I missing something? Thanks Narutaka. | |
| Mar 28, 2020 at 0:55 | comment | added | Paul Visoianu | Thanks Narutaka. I need these facts for more general Banach algebras. I could assume a little more: what if L is a maximal left ideal? | |
| Mar 26, 2020 at 2:14 | comment | added | Narutaka OZAWA | In case $A$ is a C*-algebra and $L$ is a closed left ideal, $T_L(A)$ is isometrically isomorphic to the C*-algebra $A/\ker T_L$. I guess it's not that simple for general Banach algebras. | |
| Mar 23, 2020 at 21:10 | comment | added | Paul Visoianu | The kernel is a two sided ideal, cannot equal L (a left ideal), | |
| Mar 22, 2020 at 20:12 | comment | added | Paul Visoianu | Thanks, but I do not know when this happens in general. It may happen even if the norms are not equal. | |
| Mar 22, 2020 at 19:58 | comment | added | Nik Weaver | Well, it would be easy to give examples. In "reasonable" cases the kernel of $T_L$ is $L$ and the norm of $T_L(a)$ equals the norm of $a + L$ in $A/L$. So $T_L(A)$ is isometric to $A$ and therefore complete. There will be degenerate examples where that isn't true, though. A good question would be: is $T_L(A)$ always closed? | |
| Mar 22, 2020 at 18:54 | comment | added | Paul Visoianu | I am currently studying the invariant subspaces of strictly cyclic Banach algebras and their reflexivity (as operator algebras). | |
| Mar 22, 2020 at 18:34 | comment | added | Nik Weaver | How did this question arise? | |
| Mar 22, 2020 at 17:55 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tags
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| Mar 22, 2020 at 17:55 | review | First posts | |||
| Mar 22, 2020 at 19:31 | |||||
| Mar 22, 2020 at 17:51 | history | asked | Paul Visoianu | CC BY-SA 4.0 |