Timeline for Comparison between the operator norm and the $L^1$ norm on group algebras
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 6, 2023 at 16:42 | comment | added | David Gao | Oh, I realized. It is enough to consider a generating group of unitaries to prove $P$ intertwines into $\Delta(M)$. Now this proof also makes sense to me. Thank you! | |
| Nov 6, 2023 at 9:16 | comment | added | Stefaan Vaes | I have added more details to answer the above two questions. Below I also give a more ad hoc proof that uses less heavy machinery. Nevertheless I believe that there should also be a truly elementary proof. | |
| Nov 6, 2023 at 9:15 | history | edited | Stefaan Vaes | CC BY-SA 4.0 |
More details added in response to the comments.
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| Nov 6, 2023 at 5:02 | comment | added | David Gao | Thank you for the answer! The following are probably dumb questions: first, are all unitaries in $P$ of the form $v \otimes v$? (As that seems to be needed when you say that implies $P$ embeds into $\Delta(M)$ inside $M \bar{\otimes} M$.) Also, why does $P$ contain all elements invariant under the flip automorphism? Is there an easy way to see this? | |
| Nov 6, 2023 at 4:18 | comment | added | Yemon Choi | In this context, what does "embed" mean? Is it just unitarily equivalent to an inclusion? | |
| Nov 5, 2023 at 22:53 | history | answered | Stefaan Vaes | CC BY-SA 4.0 |