There are three separate permissions that work in conjunction to control a user's ability to create or modify workspaces.
A user requires the "User Administration" category "View" and "Author Mode Eligible" permissions, as well as the "Workspace Administration" category "Workspace Author Mode" permission, in order to modify or create workspaces.
If the "Workspace Author Mode" permission is not assigned to a user, the workspace tool icons will be greyed out, resulting in the user having only read-access to any assigned workspaces.
By granting the "User Administration/View" permission, the user is able to toggle their "Workspace Author Mode" permission giving them write access as required.
Workspace Author Permission Summary
Note: All permissions mentioned in this article are set using the "Administer Users" dialog, which can be accessed from the Edit menu, the tool bar (the man standing next to the pencil) or by pressing CTRL+U