Responsa על בבא בתרא 114:16

Also, regarding your suggestion that some of the people without seats could put portable seats in the middle of the synagogue and sit there, or sit on rows of clean mats on the ground if they wish, for no individual owns anything other than his space and its entrance and exit access, but everyone owns the rest equally: They also may not do this. For even those who own seats, with access for entrance and exit, may not use that which is a path belonging to others ... just as residents of a street or [shared] yard may not use the street or yard other than in ways that residents normally use streets or yards ...