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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2010
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1007.4368 |
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| _version_ | 1866910543960342528 |
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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 |