Topologies and bornologies determined by operator ideals

The notion of topologies, introduced by Stephani[10], is useful for studying the injective hull of an operator ideal. Using Randtke’s idea(see [8,p.90] or [12,(3.2.1)and(3.2.7)]), we can characterize generating topologies in terms of seminorms which satisfy some ex-pected properties(see Lemma3.3 and Theorems3.4 and 3.9). By a well-known and usefu