Usted describe el requisito básico para una consulta de intersección.
select item.id, item.name
from item, PurchaseLog p, user u
where lower(u.username) = lower('Username1')
AND p.user_id = u.user_id
and item.id = p.itemid
and p.purchasedate between SYSDATE and SYSDATE-365
INTERSECT
select item.id, item.name
from item, PurchaseLog p, user u
where lower(u.username) = lower('Username2')
AND p.user_id = u.user_id
and item.id = p.itemid
and p.purchasedate between SYSDATE and SYSDATE-365
Esto devolverá una lista de item.id y item.name que aparecen para ambos usuarios.
