If I'm Italian could I have Jewish ancestors?

heard there large jewish population throughout italy on time, sicily. ancestors italy , curious see if of them have been jewish. maternal grandmother's family originates lazio, italy , rest of family sicily. have attached family tree see if may able identify jewish-italian surnames. know difficult based on surnames if there me has experience kind of work grateful. thank answers.

http://i955.photobucket.com/albums/ae37/giovinetti/carrafielofamilytree.jpg

i heard there large jewish population throughout italy on time, sicily. ancestors italy , curious see if of them have been jewish. maternal grandmother's family originates lazio, italy , rest of family sicily. have...

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