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Main Authors: Paul, Kallol, Das, Gopal, Debnath, Lokenath
Format: Preprint
Published: 2010
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Online Access:https://arxiv.org/abs/1007.4368
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author Paul, Kallol
Das, Gopal
Debnath, Lokenath
author_facet Paul, Kallol
Das, Gopal
Debnath, Lokenath
contents We introduce the concept of theta-antieigenvalue and theta-antieigenvector of a bounded linear operator on complex Hilbert space. We study the relation between theta-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. in \cite{19}. We show that the concept of real antieigenvalue, imaginary antieigenvalue and symmetric antieigenvalue follows as a special case of theta-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 theta-antieigenvalue. We illustrate with example how to calculate the $θ$-antieigenvalue for an operator acting on a finite dimensional Hilbert space.
format Preprint
id arxiv_https___arxiv_org_abs_1007_4368
institution arXiv
publishDate 2010
record_format arxiv
spellingShingle Computation of antieigenvalues of bounded linear operators via centre of mass
Paul, Kallol
Das, Gopal
Debnath, Lokenath
Functional Analysis
47A63 (Primary), 47B44 (Secondary)
We introduce the concept of theta-antieigenvalue and theta-antieigenvector of a bounded linear operator on complex Hilbert space. We study the relation between theta-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. in \cite{19}. We show that the concept of real antieigenvalue, imaginary antieigenvalue and symmetric antieigenvalue follows as a special case of theta-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 theta-antieigenvalue. We illustrate with example how to calculate the $θ$-antieigenvalue for an operator acting on a finite dimensional Hilbert space.
title Computation of antieigenvalues of bounded linear operators via centre of mass
topic Functional Analysis
47A63 (Primary), 47B44 (Secondary)
url https://arxiv.org/abs/1007.4368