Receiving message in iTunes "iTunes can't verify the identity of the server ...

"..."client.api.itunes.apple.com." The certificate for this server is invalid.

This was asked previously on this forum, but not really answered adequately. App Store account management window freezes at that point and must be force quit.

This seems to be part of an overall pattern of AppStore and iTunes Store failures (like asking for Apple ID password three times in a row before permitting use of the AppStore app on the desktop – just one example). What is going on?