On almost similarity results on partial isometrics, 𝛉�- operators and posinormal operators

Abstract

It is pre-eminent that equality of spectra is realized when the two given operators are unitarily equivalent or similar but not when they are almost similar. Also, projections which are 𝛼-almost similar, demonstrate that under certain conditions, they not only have equal spectra but also equal approximate point spectra. Though almost similarity property has been studied mostly, there is still gap in literature linking it directly to commuting condition for partial isometries, θ-operators and posinormal operators. This paper exhibits some primary results of such nature on the above mentioned classes of operators.