Generalization of numerical range of polynomial operator matrices
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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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