The question arose regarding a person who spent Shabbat in a hospital and did not have access to a Siddur. He was unable to recite the Shabbat Amida from memory, but did know the weekday Amida by heart, and he recited the weekday Amida. Did he fulfill his prayer obligation?
This question was addressed by the Radbaz (Rabbi David Ben Zimra, Egypt, 1480-1574), in one of his responsa (65), where he notes two divergent texts of the Rambam's (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204) ruling on this issue. According to one version of the text, the Rambam ruled that one does not fulfill his prayer obligation on Shabbat by reciting a weekday Amida, whereas according to another text one indeed does fulfill his obligation through a weekday Amida. The Radbaz reconciles the two texts by claiming that they refer to two different cases. The ruling that one fulfills his obligation by reciting a weekday Amida on Shabbat applies in a case where the individual made some reference to Shabbat in the Amida, such as if he added in the "Shema Kolenu" section the words, "Reseh Ve'hahalisenu Be'yom Ha'Shabbat Ha'zeh." Since the person made mention of Shabbat during the Amida, he has fulfilled his obligation. If, however, one recites the weekday Amida without making any mention of Shabbat, then he has not fulfilled his obligation. He would be no different from somebody who forgets to include "Ya'ale Ve'yabo" in the Amida on Rosh Hodesh, who must repeat the Amida since he did not make mention of Rosh Hodesh.
Hacham Ovadia Yosef follows this ruling of the Radbaz, in his work Hazon Ovadia (p. 352; listen to audio recording for precise citation).
Incidentally, the authorities debate the question of whether one must repeat the Amida on Shabbat if he cannot remember whether he recited the Shabbat Amida or mistakenly recited the weekday Amida. The Mishna Berura (by Rabbi Yisrael Meir Kagan, 1839-1933) ruled (265:9) that a person must repeat the Amida in such a case, as we must assume that he recited the weekday Amida, which is recited more frequently and to which he is thus more accustomed. By contrast, Rabbi Menahem Azarya of Pano contended that we may assume that the special quality of the day led the individual to recite the Shabbat Amida ("Humro Shel Yom Gorem"). This is the view accepted by Hacham Ovadia Yosef.
Summary: If on Shabbat a person prayed the weekday Amida and added a line about Shabbat such as "Reseh Ve'hahalisenu Be'yom Ha'Shabbat Ha'zeh", he thereby fulfills his obligation of prayer on Shabbat. If on Shabbat a person is uncertain as to whether he recited the weekday or Shabbat Amida, he may assume that he recited the Shabbat Amida and therefore does not recite a new Amida.
