No. The relationship between the parties has become a landlord/tenant relationship under California law, with the tenant in a month to month rental. The tenant now has all the rights any random person in a month to month apartment rental has, and the landlord has all the obligations of a landlord.
Among other things, that means the tenant can only be kicked out via formal eviction proceedings, and the landlord cannot do obnoxious things to try to drive him out.
Before renting out your place via AirBnB (or by any other means, actually) it is really important to determine how the law where your property is located determines when a renter is just a transient guest that you can kick out at will, and when the renter is a resident and your arrangement has become a landlord/tenant arrangement.
