Can a single page be assigned to a log in?

Hello, I just want to ask if pages created in Wordpress can be assigned to users on a page by page basis?
So that member user 'A' can view and edit http://www.website/pageA but can't edit pageB.
This is so a member can have and mainatain their own Supplementary Webpage.
I am trying to do this in directory using the default theme if it make any odds!
Cheers
David