Generalization of numerical range of polynomial operator matrices
Keywords:Numerical range; V-numerical range; Polynomial Matrix.
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.
How to Cite
Copyright (c) 2023 Tikrit Journal of Pure Science
This work is licensed under a Creative Commons Attribution 4.0 International License.