ahhhh... Okay
Your issue would then be with the root and not the blog itself.
If you wish, contact your host and ask them about doing a 301 from the non www root to the www root then change your internal linking. As far as Google is concerned, any "value" would probably be attributed to one or the other. If you have your preference set to the www version that's what should be used.
For example, take a look at the URL that shows up for this search...
jumbo investments blog - Google Search
They're already using the www version for the blog so changing your internal linking shouldn't be a problem for them. It would still be a good idea IMO to contact your host about the 301 for the root.
Dave