Computation of Antieigenvalues of Bounded Linear Operators Via Centre of Mass

We introduce the concept of θ-antieigenvalue and θ-antieigenvector of a bounded linear operator on complex Hilbert space.We study the relation between θ-antieigenvalue and centre of mass of a bounded linear operator and compute antieigenvalue using the relation. This follows the notion of symmetric antieigenvalues introduced by Hossein et al. (J. Math. Anal.Appl. 70:3877–3884, 2004).We showthat the concept of real antieigenvalue, imaginary antieigenvalue and symmetric antieigenvalue follows as a special case of θ-antieigenvalue. We also show how the concept of total antieigenvalue is related to the θ-antieigenvalue. In fact, we show that all the concepts of antieigenvalues studied so far follows from the concept of θ- antieigenvalue.We illustrate with example how to calculate the θ-antieigenvalue for an operator acting on a finite dimensional Hilbert space.