There is a wide, dull spot on my marble foyer where the front door opens and closes. How can this be fixed?

The marble has probably been scratched by the underside of the door. First, trim the door bottom so that it does not scrape on the marble. Then have the dull spot refinished and polished. You will probably need to start with a course abrasive(60#). Blend the area into the existing flooring by feathering out.

TIP This is a common problem with doors that have rubber weather stripping on the bottom. It may help to frequently clean the bottom of the door to remove any sand and grit that has a tendency to accumulate there.