On theta-Antieigenvalues and theta-Antieigenvectors

Details On theta-Antieigenvalues and theta-Antieigenvectors On theta-Antieigenvalues and theta-Antieigenvectors

2010-07-26

arxiv.org/abs/1007.4368v2

Mathematics

Functional Analysis

Scientific paper

We introduce the notion of theta-antieigenvalue and theta-antieigenvector of a bounded linear operator on complex Hilbert space and study the realtion between theta-antieigenvalue and centre of mass of a bounded linear operator. We show that the notion of real antieigenvalue, imaginary antieigenvalue and symmetric antieigenvalue follows as a special case of theta-antieigenvalue. We also show how the notion of total antieigenvalue is related to the theta-antieigenvalue. In fact, we show that all the notions of antieigenvalues studied so far follows from the concept of theta- antieigenvalue. We illustrate with example how to calculate the theta-antieigenvalue for an operator acting on a finite dimensional Hilbert space.

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