On a theorem of Terzioğlu

Abstract

The theory of compact linear operators acting on a Banach space has a classical core and is familiar tomany. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a numberof important connections that deserves illumination. In this paper we survey Terzioğlu’s characterization theorem forcompact maps and some of its consequences. We also prove a similar characterization theorem for Q-compact maps.