My mother lives in a retirelement complex where there are electronic doors, meaning that the doors open automatically when the sensors detect someone nearby. My question is if I am allowed to visit her on Shabbat if I know that if I go anywhere near these doors, the sensors will activate opening the doors. There is no other way to get to her using anything manual.
Walking into the sensors zone in order to activate the sensors and open the doors is prohibited. It would be a great Mitzvah if you can get the building mangers turn off the electronic doors for Shabbat; you will be preventing many Jews from violating Shabbat. As long as the electronic doors are on, you should do everything possible to visit her during the week, not on Shabbat; it will also be a great merit for your mother, sacrificing your pleasurable visit for the honor of Shabbat. If it is extremely important to visit her on Shabbat then wait until someone else walks into the building and walk in immediately while the doors are open.