I was taught that in the weekday Torah service, the ark is closed as soon as the Sefer Torah is removed, so that when we bow for gadlu lashem iti, it is clear we are bowing to Hashem and not to the ark and its contents, lest it appear, cholilla, as avoda zara. Some old timers in the minyan are not satisfied with my explanation, and want to keep the ark open. Logic is not having any effect: the ark is always closed on Shabbat as well, and if we had no other Sefer Torah, would they still bow to the empty ark? I've been challenged to provide a halacha. Assistance appreciated.
A friend wrote: I have not found this question addressed in the law codes I usually check with. Here is my take on the matter of the ark open or closed for Gaddelu:
The aron kodesh serves two purposes:
It is the repository of Torah scrolls.
It is the symbolic opening to a particularly propitious conduit for prayer. We pray with the ark open when we are especially eager for our prayers to travel quickly and directly to G-d.
Whether to leave the ark open or closed for Gaddelu depends, I think, on which function of the ark is current in your mind at the time. If it is function 1 above, you could make the case that the ark should be closed so that it does not appear that one is bowing to the Torah scrolls. But if it is function 2 above, you might well decide to leave the ark open so that these words of praise of G-d's name (symbolically) travel quickly and directly to G-d.
My teacher, the revered master Talmudist Rabbi Sha'ul Lieberman, z"l, would usually be the one to open the ark for the Torah service. He always waited until after Gaddelu to close it.