Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaThe notion of compactness plays an important role in analysis. It has been extensively
discussed on both metric and topological spaces. Various properties of compactness
have been proved under the underlying spaces. However, if we consider these sets to be
from similarity orbits of norm-attainable operators, little has been done to investigate
their compactness. In this paper, we introduce the concept of compactness of similarity
orbits of norm-attainable operators in respect to invariant topological spaces and
investigate their properties.Jaramogi Oginga Odinga University of Science and Technology, Kenya
