iTunes opens on my iMac automatically
None of the suggestions here had made any difference.  But, I kept looking and scouring the web and found (I don't remember where) what I thought, at first, was a half-assed suggestion that seems to have done the job.  The suggestion was that a "dirty" or misaligned speaker jack could be the issue.  Well, some days ago I removed the speaker plug from the iMac and, lo and behold, the constant opening of iTunes ceased.  I will eventually experiment to see if that was really the issue, but at least temporarily I'm satisfied with using the internal speakers.