E ISSN: 2583-049X
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International Journal of Advanced Multidisciplinary Research and Studies

Volume 2, Issue 2, 2022

Characterization of Numerical ranges of Matrix Operators in Hilbert Spaces



Author(s): Benard Okelo, James Mbugua Ngigi

Abstract:

Let H be a Hilbert space. Let A be a 3 X 3 complex matrix whose numerical range, W (A) , is an ellipse. Also let W(A) ⊂ ?  where ? is a convex subset of the complex plane. We determine the value of ψD(A) by reducing it to the case of 2 X 2 matrix with elliptical numerical range.


Keywords: Matricial Operator, Hilbert Space, Holomorphic

Pages: 171-183

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