Can we oxidize oxygen?
Oxygen can be oxidized. However, it is uncommon due to its high electronegativity. In fact, it is highest second only to fluorine. This makes it extremely difficult to remove electrons from oxygen, thus making it hard to oxidize.

One definitive example of oxygen being oxidized is oxygen difluoride. This exception is even listed on many lists of oxidation state rules (see: oxidation states).

And of course, if you go beyond stable molecules, it is possible to ionize oxygen with an electrical charge.