Should Schmidt Resign from Apple's Board?

Google and Apple seem headed on a collision course with their respective telephony products, leading to sentiment that Google CEO Eric Schmidt should resign his seat on Apple's board.

The crux of the biscuit is Android, the Google-sponsored smartphone operating system sold to phone manufacturers as an alternative to the iPhone. Now that Android may show up in netbooks from HP, it will come into competition with the Mac too.

Some observers note that Google is also a major backer of Clearwire, "a would-be competitor to AT&T on the wireless data front, though that will take some time." Indeed, by the time Clearwire becomes a real threat to AT&T, Apple may have moved away from its exclusive deal with AT&T.

Nevertheless, BusinessWeek Apple blogger Arik Hesseldahl agrees with CNBC analyst Jim Goldman that Schmidt may soon be recusing himself from a disproportionate number of board discussions.

"I like the idea of having Schmidt on Apple's board, and I like the idea of Apple and Google working together as much as possible. But the potential for conflicts of interest appears to be mounting."

From Google's perspective, Schmidt's membership on Apple's board is a good thing. I can see where it might be a problem from Apple's perspective because it's involved in far fewer businesses--an increasing number of which involve Google either as a partner or a competitor.

What's your take?