I personally don't think he could do any banning that would hold up in court. There are a couple of things that he could do though (and that would actually be good).
1. He could order tough enforcement of the required reporting of mental illness to the NICS system. Way too many wackos don't get properly reported.
2. He could order the Justice Dept to take a hard line on convicted felons who get caught with guns. They can't re-offend if they are locked away for long sentences.
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