Operating Electric Doors on Shabbat

Dear Rabbi Is it permissible to activate an electric door on Shabbos simply by standing in front of it?

Can I open an electric door on Shabbos, just by standing in front of it?
Your question stems from an understanding that it is only forbidden if one performs the actual melacha. However, we will learn that sometimes, even without doing any active melacha, it is still forbidden 'min haTorah' to do it. So, what are the guidelines?
The Gemara in Tractate Bava Kamma, page 60a, writes, and I quote:
תלמוד בבלי מסכת בבא קמא דף ס עמוד א
רב אשי אמר: כי אמרינן זורה ורוח מסייעתו - ה"מ לענין שבת, דמלאכת מחשבת אסרה תורה, אבל הכא גרמא בעלמא הוא, וגרמא בנזקין פטור
Rav Ashi said, "When do we say that one scatters seeds and the wind assists him - this applies to the matter of Shabbat, where the Torah forbids 'intentional work' (melachet machshevet). However, here [in the case of damages] it is merely indirect causation, and indirect causation in the context of damages is exempt."
The Talmud speaks about the difference between Shabbat and damages, stating that one of the melachot forbidden on Shabbat is bor’er, which in agricultural settings involved separating chaff from wheat. After threshing the grain, creating a mixture of grain and empty chaff, one would wait for a light breeze. They would then toss the mixture into the wind; the lighter chaff would blow away, and the heavier grain would fall. This method of selecting the wheat from the chaff is called zoreah le’ruach and is considered a form of bor’er, which is forbidden on Shabbat.
So, the Talmud writes that even though the act of bor’er was not done solely by the person but rather was assisted mainly by the wind, on Shabbat the core of the melacha is not necessarily whether you did the entire melacha but whether your intention was carried out by the action that took place. This is called ‘meleches machsheves asurah min haTorah’ – the Torah forbids a melacha that you initiated and achieved the results, even though you did not actually carry it out yourself. As long as this is considered the standard way of performing the melacha, as we learned from the Talmud above. This is a chidush of hilchot Shabbat, since when it comes to liability in damages, one would not have to pay (through a bet din) since such an action carried out by the wind is considered gerama when it comes to damages.
Based on the above, we can now understand when one wants to enter through an electric door that by coming close to the entrance, one is activating the sensors, and it will then automatically open. This is forbidden on Shabbat, as explained earlier on the subject of zoreh le’ruach, since you initiated this melacha to get this outcome, and this is how it is done; it is called meleches machsheves and is forbidden.
Now, in a case where you were in a hotel, what are you supposed to do? The best option is to wait for someone to pass. However, this is where it gets complex since it depends on whether he is Jewish (unfortunately, non-observant) or not. Let’s organize it:
A non-observant Jew who opens the door: Some poskim write that it is forbidden to enter after him since we have a general prohibition from benefiting from ‘Ma’aseh Shabbat,’ and since the door was opened by a Jew, one cannot benefit from his action. However, many poskim write that this is not considered benefiting from ‘ma’aseh Shabbat’ since it is just a removal of an obstruction, so it is not considered having an active benefit from the melacha, and so it would be permitted. Le’halacha, one can rely ‘beshat hadchak’ on this opinion.
If it was opened by a non-Jew: It is permitted to go out through the door with him since he opened it for his own purpose, and one may benefit from it. However, lechatchillah, one should try, if it is a wide door that opened, to go past the door before the non-Jew, since if one goes after him, then the sensors will be activated by the Jew since it is connected to sense when the last person goes past in order to close the doors. This is only lechatchillah because even if the sensors will sense the last person, since the Jew has no benefit from it, it is considered Einoy Mischaven since I have no interest in it.
Of course, once the doors start to close, it is forbidden to go past since this will activate the doors to reopen.
Wishing you well.

1. Talmud Bavli, Tractate Bava Kamma, 60a