It seems like Google only indexes those urls with your preferred domain in your google sitemap. if you specify domain without www, all the search results will be based on your domain without www. Therefore those with www urls are not indexed. Am I right?
I don't think so, only if you have inbound links for pages like www.yourdomain.com/yourpage.htm, this page will be also crawled and indexed by google.
You'll notice that PR only appear in eg: http://yourdomain.com if you specify your preferred domain as yourdomain.com and PR will be zero when you visit http://www.yourdomain.com.
www and not www can be considered as different hosts. As a matter of fact, they are different hosts even if they usually points to the same location. You are encouraged to choos one host and use it by default. Sitemaps links should point only to this host and you should redirects other requests with a server side configuration.