NOTIONS OF CONTINUITY FOR FINITE RANK MAPS IN THE SPACE OF NORMAL OPERATORS

Abstract

We show that a natural extension of a continuous finite rank operator to an arbitrary Hilbert space is continuous. We also give sufficient conditions to calculate delta- epsilon numbers in all the domains of T. In addition, we characterize the concept of uniform continuity in terms of delta- epsilon function and finally show that finite rank operators preserve Cauchyness.