I'm sorry, how do they have a monopoly on portable music players? They have a very popular player, of which they are the sole manufacturer, and require you to use their software.
The free market has plenty of alternatives, though not as good if you ask me, if you do not like their solution you are free to purchase another. There's nothing monopolistic about having a hugely successful product.
You're allowed to have a monopoly, you're not allowed to abuse it. If Apple ordered mp3hardware stores to stop selling other brands or Apple would raise it prizes, that would be abuse.
(a) The GP of my comment asserted that automatically installing Safari when you install iTunes was monopoly abuse. I think they at least have a point.
(b) Apple has about 2/3 of the paid music download market and 3/4 of the MP3 player market. They block other MP3 players from talking to iTunes, and other desktop software from talking to the iPod. I think that's probably abuse: they're using iTunes's dominant market position to protect the iPod's dominant market position, and vice versa.
They leveraged one monopoly to create another instead of trying to promote IE on its merits, and implemented IE with insider knowledge of how Windows works, and did various other things like coercing OEMs. Those are the things that got them in trouble, not simply having the OS monopoly.
Portable music players isn't such a meaningful category when you consider most mobile phones can also play music; plus just other music listening devices in general.
It may vary from nation to nation, but under US law the relevant act here is the Sherman Antitrust Act, which deals with single-firm anti-competitive behavior.
We'd have to wade through a lot of case-law here, but if you'll permit me the ability to speak without excessive sourcing (most of this can be found supported and sourced on Wiki)...
The courts have made a distinction between an innocent and a coercive monopoly. Where innocent monopolies, as you may argue but I disagree, are what Apple has in the music player space. These are not illegal. It would need to be shown that Apple has conspired in some way to grow and maintain their market position in a way to be detrimental to consumers and other producers.
Right now another consumer electronics company could: a) produce a new unit with a high quality software, b) sell it at a competitive price point to Apple, c) create a product very similar to the iPod itself, d) there already exist many other competitors. To me these factors suggest Apple does not have a monopoly but a very successful product.
And I'd submit as noted above, even if you found Apple to have a monopoly, I do not believe it would qualify as coercive under US law.
As noted in this thread, market share is not so much the issue, as barrier to entry.
The free market has plenty of alternatives, though not as good if you ask me, if you do not like their solution you are free to purchase another. There's nothing monopolistic about having a hugely successful product.