Generalization of numerical range of polynomial operator matrices

Authors

  • Darawan Zrar Mohammed
  • Ahmed Muhammad

DOI:

https://doi.org/10.25130/tjps.v28i1.1268

Keywords:

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.

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Published

2023-02-20

How to Cite

Darawan Zrar Mohammed, & Ahmed Muhammad. (2023). Generalization of numerical range of polynomial operator matrices. Tikrit Journal of Pure Science, 28(1), 75–81. https://doi.org/10.25130/tjps.v28i1.1268

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