Irreflexive Banach spaces are imperfect

It is shown that irreflexive Banach spaces are imperfect: thus the “perfect” spaces are exactly the reflexive Banach spaces and “mixed” spaces do not exist. This paper is part of the author’s M.Sc. dissertation, performed under guidance of Dr. D. Amir at the Technion — Israel Institute of Technology. The author wishes to thank Dr. Amir for his help.