What is "gattilusi"

The Gattilusi (singular Gattilusio) were a powerful Genoese family who controlled a number of possessions in the northern Aegean from 1355 until the mid 15th century. Anthony Luttrell has pointed out that this family had developed close connections to the Byzantine ruling house of the Palaiologos—"four successive generations of Gattilusio married into the Palaiologos family, two to emperors' daughters, one to an emperor, and one to a despot who later became an emperor"—which could explain their repeated involvement in Byzantine affairs.