How could the building you describe be assessed at only 1.4 million? In my city, a single condo that rents for $4k/mo would be assessed higher than that.
I'm so glad you asked. In 1978 Californians passes Proposition 13, written for and sponsored by the Los Angeles Apartment Owners' Association, which says that property assessments may not increase by more than 2% per year or CPI, whichever is less. Property tax rates may not exceed 1% of assessed value. So the max theoretical assessment of a building bought for 1.05 million twenty years ago is 1.56 million.