Generalization of numerical range of polynomial operator matrices
DOI:
https://doi.org/10.25130/tjps.v28i1.1268Keywords:
Numerical range; V-numerical range; Polynomial Matrix.Abstract
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.
Downloads
Published
How to Cite
License
Copyright (c) 2023 Tikrit Journal of Pure Science
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
