Just a brief clarification, you should view much of the Italian architecture that seems eastern influenced not as Islamic influenced, but eastern-Roman/Byzantine influenced.

Much of Islamic architecture in its early days was borrowed straight from the Byzantine textbook. It wasn't til much later during the Abbasid period that it acquired a Byzantine/Persian fusion, and from then on its own particular style.

But with that said, the short answer to your question is simply, Italian architecture represents their geographic position as a key node in Mediterranean and European cultural interaction and foreign occupation.