Now the book has been accessed it is locked to the Adobe account/ID in use at the time (eg the Adobe account you registered for Administrator).
You can't change authorization on the book itself once it has been accessed (unless you make another purchase/loan or some special arrangement with the vendor).
The registration/authorization is separate for each user (this may not be convenient in your case but is convenient for many situations).
What you need to do is go through the authorization process again on the user account, using the same Adobe ID you used on the Administrator account.
Copying in a problem people sometimes have below, just in case it might save the time of an extra interaction in this thread ...
ignore this unless you fine you can't go through the authorization process on the user account.
Sometimes ADE gets its registration/activation confused and in a semi-authorized state.
Uninstalling and reinstalling does not help, and indeed installation can even trigger this state.
Unfortunately, it often then gives misleading error messages about what is wrong.
A common incorrect message informs you that the ID is already in use on another computer and cannot be reused.
Another is "E_AUTH_NOT_READY"
This can often be resolved by completely removing any authorization using ctrl-shift-D to the Library screen on ADE (cmd-shift-D if on Mac).
Restart ADE, and then reauthorize with your (old) Adobe ID.
In extreme cases on the mac, the following extra step has helped some people. Navigate to /Users//Library/Application Support/Adobe/Digital Editions and drag the activation.dat file to the trash. If you are using 10.7, see Access hidden user library files | Mac OS 10.7 Lion. http://forums.adobe.com/thread/1265248?tstart=0