# On a theorem of Terzio\u{g}lu

## TL;DR

This paper explores Terziogu's characterization theorem for compact linear operators on Banach spaces and extends it to cases with an approximation scheme, highlighting its theoretical significance.

## Contribution

It provides a detailed analysis of Terziogu's theorem and introduces a similar characterization for Banach spaces with an approximation scheme.

## Key findings

- Characterization of compact operators via Terziogu's theorem
- Extension of the theorem to spaces with approximation schemes
- Insights into the structure of compact maps on Banach spaces

## Abstract

The theory of compact linear operators acting on a Banach space has such a classical core and is familiar to many. Perhaps lesser known is the characterization theorem of Terzio\u{g}lu for compact maps. In this paper we consider Terzio\u{g}lu's theorem and its consequences. We also give a similar characterization theorem in case where there is an approximation scheme on the Banach space.