Wow, you've got some interesting answers. You should do your own research or talk with an agent that has worked in income property in Los Angeles.
Here are the facts:
The city of Los Angeles has a rent control ordinance (see link).
I called the RSO office, and Hollywood IS part of the City of Los Angeles (West Hollywood is a separate city), so you are looking at the potential for rent control.
The ordinance applies to only properties of a specific age
To be subject to the RSO of the City of Los Angeles, a property must meet the following three criteria:
1. The property must be within the City of Los Angeles; and
2. There must be two or more units on the lot; and
3. The building must have a Certificate of Occupancy issued on or before October 1, 1978. (In the case of mobile homes and mobile home pads, the park must have been issued a permit to operate before February 10, 1986).
In order to raise rents above the permitted rate there are very strict regulations, which basically prohibit you from evicting tenants solely to increase rent rates.
Another way to say this is that if the building was built before 1978 the rents WILL be under market, by definition, and there is absolutely nothing you can do.
If you are serious about investment property I'd be happy to discuss your plans and see if I can help you.