CA Rent Control when no lease exists

[David Coe]

I'm considering buying a duplex that has long-term tenants substantially under market rents. There are no leases in place, just a handshake agreement from tenant to owner. Listing agents says rents have not been raised in 20 years. Currents are 30% of what market rents should be. If I buy the property, are these outdated rents my new basis? How would I get the rents back to market?