Byzantium gradually became the theater of Islam's spread, which included territories of Eastern Europe and Russia.

While Byzantium did face Muslim invasions and encounters with Islamic armies, it is not accurate to say that Byzantium itself became the theater for the spread of Islam into Eastern Europe and Russia. The spread of Islam into these regions occurred primarily through the Turkic and Mongol invasions centuries after the decline of Byzantium.

During the early Islamic period, the Byzantine Empire, also known as the Eastern Roman Empire, faced several Arab Muslim invasions. These invasions were part of the larger Muslim conquests, which aimed to expand the territories ruled by the new Islamic Caliphate. Byzantium successfully resisted many of these incursions, particularly during the 7th and 8th centuries.

However, Arab Muslims did establish some footholds in the eastern Mediterranean region. The most notable of these was the conquest of Syria, Palestine, and Egypt, which had been previously under Byzantine rule. These territories later became the heartland of the Umayyad Caliphate, and Islam became the dominant religion in these areas.

It is important to note that the spread of Islam into Eastern Europe and Russia occurred through later invasions and migrations by Turkic and Mongol peoples. These groups, such as the Seljuks, Khwarazmians, Mongols, and Ottomans, were influenced by Islam and brought the religion with them as they expanded their empires.

The Turkic Ottoman Empire, in particular, played a significant role in the spread of Islam into Eastern Europe. The Ottoman Turks conquered Constantinople, the capital of the Byzantine Empire, in 1453, effectively ending Byzantium. Over the next few centuries, the Ottoman Empire expanded into areas such as the Balkans, Greece, and parts of Eastern Europe, gradually spreading Islam to these regions.

Similarly, the Mongols' conquest of Russia in the 13th century led to the establishment of the Golden Horde, a Mongol state that ruled over parts of Eastern Europe. While the Mongols themselves did not convert to Islam, they facilitated its spread by promoting the religion and allowing Muslim merchants and scholars to operate within their empire. The Mongols' influence eventually led to the conversion of some Russian principalities to Islam.

In summary, while Byzantium faced Muslim invasions, it did not become the theater for the spread of Islam into Eastern Europe and Russia. The spread of Islam into these regions was primarily a result of later Turkic and Mongol invasions, which occurred after the decline of Byzantium.