How to show a View field depending on roles?
Check the permissions for the role of "administrators" (D7: admin/people/permissions, D6: admin/user/permissions).  If the user has permission to edit the node, the edit link will be visible, if not, the edit link will not be shown. Views takes into account a user's (role's) permissions.

D7 Example:  Say you are creating a list of Stories. If the administrators role has the permission "Story: Edit any content", the user will be able to see the "Edit" link for that node in the listing, while if the role only has the permission "Story: Edit own content" the "Edit" link will only be shown if the current user created the Story.