Tunics like this are typical of mens clothing in the Eastern Roman Empire from late Antiquity to the eleventh century. At some point prior to the tenth century Romans adopted the ancient Persian practice of opening the tunic down from the left side of the neck. True Romiosi custom (as defined by the conventions of elite art) wore it as shown, while the art of other nationalities influenced by Constantinople show that it was commonly worn in a way that made a feature of it. (Mouse onto the picture for detail of the collar.)1
The turban had gained popularity among Roman men in the eighth century and persisted for centuries. It was never quite accepted as properly Roman and so despite being refered to quite often in literature, it is relatively rarely illustrated. A video showing a basic method for tieing a turban here (6.5Mb).
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1) Shown on the Church of the Holy Cross at Aghtamar in Armenia, and a Umayyad carved chest.