howto calculate column means in data frame

Long story short, I have a big iterative procedure that produces a long
list of data.frames such as the one called
"results" here.  Is there an easy way to produce a similar list of
data.frames comprised of the mean of each of the
columns in results, such that it ends up like the one I've shown in
"resultsmean" below?

I've tried apply and lapply, still not got the correct arguments.  As
usual, TIA.

Jim

results

[[1]]
       name    LOR23       BIA23       MSE23          H0R23
1 0.2111122   -1.012228   -0.095937    0.035650        1.00
2 0.2111122   -0.836300    0.079991    0.042322        0.75
3 0.2111122   -0.518631    0.397659    0.214593        0.50


[[2]]
       name    LOR23       BIA23       MSE23          H0R23
1 0.2211122   -0.724630    0.191660    0.051308           1
2 0.2211122   -0.781812    0.134478    0.033872           1
3 0.2211122   -0.522109    0.394181    0.164628        0.75


would like

resultsmean

[[1]]
       name    LOR23       BIA23       MSE23          H0R23
1 0.2111122   -0.78333    0.12734     0.097160        0.75

[[2]]
       name    LOR23       BIA23       MSE23          H0R23
1 0.2211122   -0.67566    0.2400      0.08266         0.916