I cannot speak to Armenian or Syrian communities specifically, but it did develop significant settlements of "merchant colonists" from the Italian maritime republics like Venice, Genoa, Pisa, and Amalfi.

The republics were granted trading privileges in the capital and other parts of the empire. In addition, they were each granted their own districts of the city by the Byzantine emperors, usually near the harbor, where their citizens lived and were able to conduct their mercantile endeavors. These communities were typically quite invested in the city's fortunes, and at least in the case of the Venetians and Genoese, remained in some numbers even until the final Ottoman siege and conquest in 1453, where they took part in the defense efforts.

There was even a similar small settlement of Muslim traders, although I haven't been able to look up of what extraction from the Islamic world they were.

It is likely that at their greatest extent, there were 10,000-20,000 or more Italians living in the city, at a time when its total population was perhaps 500,000.