Italy and the East

In our discussion of the Italian Renaissance, Mrs. Quinet made several references to Ottoman influences on European art.  I was wondering in what historical context these influences could be placed.
I don't have any books on the subject, and I found fairly little specific information online.  In general, it seems that the Italian city-states, particularly Venice, were alternately at war with and trading with the Ottomans throughout the high middle ages.  The focal point of the relations and trade between the Ottomans, the Byzantines, and the Italians was Constantinople, later Istanbul.  The Byzantines had the oldest claim to the city, but the Venetians actually controlled it after the Fourth Crusade (in which the "Crusaders", sailing from Venice shortly after the Byzantines had expelled Venetians from Constantinople, turned on their Christian erstwhile allies and took the city)  for the first half of the 13th century, and after 1453 it was an Ottoman territory.  The Venetians--who had territories in the Balkans and throughout the eastern Mediterranean--were intermittently in conflict with whoever wanted control of Greece; they had an antagonistic relationship with the Byzantines, and by the apogee of Ottoman power were in constant conflict with them too.
However, Venetians also controlled the trade--in metalwork, incense, and most of all pepper--with the East, and a significant cultural transfer in the interwar periods was inevitable, as we saw in, for example, the Venetian portrayals of the Virgin Mary.
Relations really soured, however, and this transfer ended around the time of the Italian Renaissance.  In the middle of the 16th century, the Ottomans expanded into Catholic Europe: they were famously at the gates of Vienna by 1529, and under the leadership of the supremely competent Suleiman the Magnificent.  Unfortunately for the Ottomans, Vienna was under the control of the Hapsburgs, who at that time were also at their height and also had a competent and powerful leader in Charles V, who finally broke their advance.  The Popes of the time were simultaneously facing this existential threat and that of the Reformation, and the Italian city-states increasingly turned agains the Ottomans, culminating in the Battle of Lepanto (1571) in which a combined Italian fleet defeated the Ottomans in the Gulf of Corinth.