Political status of the Abbasid Caliphate in beginning relationship with the Seljuqids

What has been inferred from the references and sources, is that by the advent of Seljuqids, Abbasid Caliphate was severely weakened and lost its political position in many Islamic territories. This study is to answer the issue that unlike many researchers beliefs, Abbasid Caliphate was not considered as a weak,shaky political system versus Buwayhid rulers and at the start of its relations with Seljuqids it could improve the political position of caliphate for various reasons. This study has been directed based on the historical and analytical data and its results show that the two last caliphs of Buwayhids era al-Qader Billah (381-422) and al-Qaim Beamrellah(422-467), were among those who made a lot of efforts to regain the caliphate's lost identity, as we can observe the revival of caliph's authority, at least in Iraq territory.