David Barton Gym has leased a 20,100 square-foot space in the Southeast Financial Center. There is no opening date yet, but construction and equipment installation have begun on the space. The gym will open at the top of the building's 15-floor annex and will be available for use for those who live and work in the area near Miami's Central Business District. Services include fitness classes and trainer workouts. RELATED CONTENT: YouFit Health Clubs and four other companies to open at Lauderdale…