α–almost similar operators

Abstract

The study focuses on α–almost similar operator which is a new concept of the operator theory and also some basic concepts related to the concept α–almost similar.The study also defines a new concept called β–operator which is an expansion of the concept θ–operator and the relationship of this concept with the α–almost similar.At the end of this research, we study some important relationships among similar, unitarily equivalent, and almost similar on the one hand and α–almost similar on the other.