I needed some information about the intersection of the kernels of invariant means on hypergroups. So I read the discussion made for the question " The kernel of all invariant means " which answer my question in the case of groups. It seems that it is somehow applicable for hypergroups. Now my question is "Does the kernel of an invariant mean on a hypergroup include strictly positive functions?"
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$\begingroup$ Is the answer positive or negative for the case of groups? $\endgroup$ – Yemon Choi Oct 31 '15 at 15:37

$\begingroup$ The last question for groups is indeed unknown for me but at least the characterization of the intersection is available. $\endgroup$ – Golab Oct 31 '15 at 15:42

$\begingroup$ Surely you should work out what the answer to your question is for groups, before trying to work out what happens for hypergroups? Or are you only interested in certain kinds of hypergroups? $\endgroup$ – Yemon Choi Oct 31 '15 at 16:26

$\begingroup$ Thank you. No special kind of hypergroups is taken. But there are special strictly positive functions that I am interested in knowing whether they have nonzero means. $\endgroup$ – Golab Nov 1 '15 at 6:29