Generalization of numerical range of polynomial operator matrices
Suppose that is a polynomial matrix operator where for , are complex matrix and let be a complex variable. For an Hermitian matrix , we define the -numerical range of polynomial matrix of as , where . In this paper we study and our emphasis is on the geometrical properties of . We consider...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Tikrit University
2023-02-01
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| Series: | Tikrit Journal of Pure Science |
| Subjects: | |
| Online Access: | https://tjpsj.org/index.php/tjps/article/view/1268 |
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| Summary: | Suppose that is a polynomial matrix operator where for , are complex matrix and let be a complex variable. For an Hermitian matrix , we define the -numerical range of polynomial matrix of as , where . In this paper we study and our emphasis is on the geometrical properties of . We consider the location of in the complex plane and a theorem concerning the boundary of is also obtained. Possible generalazations of our results including their extensions to bounded linerar operators on an infinite dimensional Hilbert space are described.
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| ISSN: | 1813-1662 2415-1726 |