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Jun 5, 2020 at 20:11 comment added Matthew Daws @YemonChoi I guess Runde's result is not a million miles away from what I had in mind. Thanks for reminding me of it! Although the proof, via Proposition 4.1, is again a duality argument...
Jun 5, 2020 at 16:57 comment added Yemon Choi Ah, I think I misunderstood your question, never mind.
Jun 5, 2020 at 16:48 comment added Yemon Choi Hi Matt, regarding your footnote/question: are you looking for something which doesn't mention algebraic properties of $L^1({\mathbb G})$? Perhaps Theorem 4.4 of Volker's paper arxiv.org/abs/math/0506493 ?
Jun 5, 2020 at 15:42 history answered Matthew Daws CC BY-SA 4.0