Al-Awza'i (may Allah have mercy on him) said that Qatadah bin Di'amah (may Allah have mercy on him) wrote to me that Sayyiduna Anas bin Malik (may Allah be pleased with him) told him that he prayed behind the Prophet (peace and blessings be upon him), Abu Bakr, Umar and Uthman (may Allah be pleased with them). All of them used to begin the prayer with 'All praise is for Allah, the Lord of the worlds' [Surah al-Fatihah: 2]. They did not recite 'In the name of Allah, the Most Gracious, the Most Merciful' [Surah al-Fatihah: 1] at the beginning of the recitation or at its end.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2414